(i) 49° (i) a = 130° ; find b. asked Jan 31, 2018 in … 2. = 90° – Question 44. Calculate: (i) Angle BEC, (ii) Angle BCD, (iii) Angle CED. (ii) ∠AOB + ∠BOC = 97° + 83° = 180° ⇒ The sum of adjacent angles AOB and BOC is 180°. 3x + 8x + 4—28 = 108. (iii) Supplementary angles ? Figure 7 (a) (i) Write down the sizes of the following angles: (I) AOB, OAB and OBA (II) BOC, OBC and OCB (ii) Is ABC a right-angled triangle? Find x. Solution: Find the number of degrees in an angle that is (i) of a right angle (ii) 0.2 times of a straight line angle. Answer, Two supplementary angles are (5x – 82°) and (4x + 73°). ∠BOC + ∠DOC = 180° 125° + ∠DOC = 180° ∠DOC = 18 In the following figure, ∠AOB and ∠BOC are. Answer, The measures of two complementary angles are (2x – 7)° and (x + 4)°. Answer, Write the complement angle of : supplementary angles. A O C. Answer, Add : (ii) x° 13. A b 2 in the following figures aob cod and eof are. Answer, The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. (ii) 6 O’clock complementary angles. 3x + 4 + 8x —28 = 108. Since OD bisects AOC, and since AOD is 4x, then DOC is also 4x. Each figure given below shows a pair of parallel lines cut by a transversal For each case find a and b giving reasons. (i) its supplementary angle. (ii) its complementary angle. (iii) ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. THINK, DISCUSS AND WRITE 1. Can two adjacent angles be supplementary? If the ray in the middle creates two equal angles, ... then m∠AOB + m∠BOC … Answer: (c) Explanation : ∠ AOB = 360° – 60° = 300°. Again, by degree measure theorem ∠BOC = … adjacent angles. (iii) Name all the pairs of adjacent angles. (iii) 9 O’clock Answer, For an angle y°, find : Answer, Two supplementary angles are in the ratio 7 : 11. (4 marks) (b) Find the area of ABC. (ii) ∠BOP = …….. Answer, In the figure, given below name : (iv) two reflex angles. Answer, Find the angle formed by the arms of a clock at: (∠ AOB + ∠ BOC = 180°) r = 90° – x. 4. Therefore Angle FOG = Angle COG. ∠AOB = 60° ∠AOB, ∠AEB and ∠AFB are angles subtended by an arc AB at the FK centre and at the remaining part of the circle. (ii) that is equal to its supplement ? (i) If x = 53°, find y. (iii) the value of y° if its supplement is four times its complement. find : angles COD and BOD. Lines and Angles Class 9 Extra Questions Very Short Answer Type. Angle ∠ AOB = 80° and ∠ ACE = 10°. Since OC bisects AOB, and since AOC is 8x, then BOC is also 8x. Answer, Find the angle that is three times its complementary angle. This preview shows page 43 - 49 out of 49 pages. Definition of perpendicular lines. (i) ∠BOD ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. (i) the complementary angle ... Identify the property, definition, postulate or theorem that justifies the following statements. (i) ∠AQB = …….. (i) 29° 16′ 23″ and 8° 27′ 12″ (a) ∠AOB and ∠BOC (b) ∠BOD and ∠BOC Justify your answer . Answer, Find the angle : Extra Questions for Class 9 Maths Chapter 6 Lines and Angles with Solutions Answers. (iii) (x – 30)° (iv) The reflex angles in the given figure are, ∠BOC and ∠DOA, Reflex angle BOC = 180 0 + 68 0 = 248 0. (ii) the complement and the supplement of the angle obtained above. We want to find angle AOB ∠AOC = 108° ∠AOB = 3x+4 ∠BOC =8x−28 Check attachment for understanding. Explain your answer. (iii) a = 5/3 right angle, find b (iv) reflex angle BOD Theorem 1: Prove that the sum of all the angles formed on … Answer, Two complementary angles are in the ratio 8 : 7. (ii) vertically opposite angles. Answer, In the given diagram, ABC is a straight line. Find whether or not the exterior arms OA and OC are in the same straight line. ∠DFG and ∠JKL are complementary angles. Find the angles. none of these. 29. The red arc indicates angle BOF which is given as 120°. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. Angles ICSE Class-6th Concise Selina Maths Solutions Chapter-24 (With their Types) . Answer Can two obtuse angles form a linear pair? 30. Which of the following statements is false? (iv) 12 O’clock (ii) b = 200 ; find a. ⇒ The exterior amis OA and OC are not in the same straight line. then ∠CDB is a right angle. Name four rays shown. Can two adjacent angles be supplementary? Find a, b, c and d in the figure given below . (i) straight line angles. (iii) which angle is obtuse ? (ii) in the exterior of the angle PQR. Answer, In the given figure, AOB is a straight line. (i) 3 O’clock (ii) ∠PQS = 110°; find ∠RQS (i) 45° Answer, Two complementary angles are in the ratio 7 : 8. 11x = 108 + 24. (i) that is equal to its complement ? In each case given below draw perpendicular to AB from an exterior point P. (Leave the answer in surd from.) Answer. In the given figure ; AOC-is a straight line. (i) Adjacent angles ? (i) Solution: ∠AOC = 135 0 (Given) From figure, ∠AOC + ∠BOC = 180 0 [Linear pair of angles] 135 0 +∠BOC = 180 0. or ∠BOC=180 0 −135 0. or ∠BOC=45 0. Also ∠AOB + ∠BOC = 180° ∴ ∠AOB and ∠BOC are supplementary. OA and OC are in the same straight line. In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° . ⇒ The sum of adjacent angles AOB and BOC is 180°. In the given Fig 5.10, are the following adjacent angles? Find x. Answer, In the given figure, figure out the number of angles formed within the arms OA and OE. (ii) ∠BQP = …….. Since ∆AOB, ∆BOC, ∆COD, ∆DOE, ∆EOF ∴ Each angle is equal to 60°. 11x — 24 = 108. (i) ∠SQR = 75° ; find ∠PQS. Answer, In the given figure if : What are the names of three planes that contain point G? (i) the angle Answer, Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles. (iii)∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°.⇒ The exterior amis OA and OC are not in the same straight line. Pages 49. (ii) 9° 45’56” and 73° 8′ 15″ ∠AOB + ∠BOC = ∠AOC. If m∠AOC=85°, m∠BOC=2x+10, and m∠AOB=4x−15, find the degree measure of ∠BOCand∠AOB. Find x. Angle AOB=x+3, angle AOC=2x+11, angle BOC=4x-7 Get the answers you need, now! (3 marks) (c) Are the areas of OAB and OBC the same? Solution: No, the sum of the measures of two obtuse angles is more than 180°. a b 2 In the following figures AOB COD and EOF are straight lines Find the. Question 3. (ii) Name all the pairs of vertically opposite angles. (ii) Complementary angles ? Answer. (i) angle BOC Question 1. If angle AOB = 28, Angle BOC = 3X-2, and Angle AOD = 6x... and if Angle AOD = a total of 110 degrees. ∠IQG b. Since OE bisects AOD, and since AOE is 2x, then DOE is also 2x. If an angle is half of its complementary angle, then find its degree measure. Given: Δ ODC ∼ Δ OBA ∠ BOC = 125° ∠ CDO = 70° To find: ∠DOC, ∠DCO and ∠OAB Solution: Here, BD is a line, So, we can apply linear pair on it. Name an angle supplementary to ∠MQI. Using the angle sum property ∠AOB + ∠OAB + ∠OBA = 180 o. (i) three pairs of adjacent angles. (m) 56° 38′ and 27° 42’30” The given diagram shows two adjacent angles AOB and AOC whose exterior sides are along the same straight line. Therefore, we have six equilateral triangles as shown in the figure. In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of : ( i ) AOB, (ii) ACB, Angle AOB = 128° Half of it is angle AOC = 128/2 = 64° = Angle BOC From the last condition → Line segment OG bisects angle FOC. Melissa writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: Melissa's proof. Class 9 Maths Chapter 8 Lines and Angles Exercise 8.2 is based on topics such as some angle relations and linear pair of angles. For triangles AOB and COD, angle … Find ∠DOC, ∠DCO and ∠OAB. 3. (ii) If ∠BOC = ∠DOC = 34° and ∠AOD = 120° ; (iv) Name all the reflex angles formed and write the measure of each. (iv) 20° + y° In the adjoining figure, ∠AOC and ∠BOC are two adjacent angles whose non-common arms OA and OB are two opposite rays, i.e., BOA is a line ∴ ∠AOC and ∠BOC form a linear pair of angles. Ex 6.3, 2 In figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. (ii) the supplementary angle Show that the points A, 0 and B are collinear. Answer, In the given figure, lines AB and CD intersect at point O. Answer, In the given figure, PQR is a straight line. Find the value of x. 12. (ii) ∠AOB + ∠BOC = 97° + 83° = 180°⇒ The sum of adjacent angles AOB and BOC is 180°.∴ The exterior arms OA and OC are in the same straight line. Question 2. If : Find the angles. ∴ The exterior arms OA and OC are in the same straight line. In the figure given below find the measure of the angles denoted by x, y, z, p, q and r. In the given figure find the angles shown by x, y, z and w. Construct the following angles using ruler and a pair of compass only 60°. Answer, For an angle x°, find : Then what is the measurement of Angle BOC and Angle AOD Name the pair of angles forming : a. 11. (v) reflex angle COE. [1998] Answer 44 Answer, In the given figure : Find the angles. (iii) obtuse angle BOD Since, the sum of adjacent angles AOB and COB = 180°. Can two obtuse angles be adjacent angles? From the attachment, we notice that the sum of angle AOB and angle BOC equals to angle AOC. In AOB. (ii) ∠AOC (iii) If ∠AOB = ∠BOC = ∠COD = 38° Answer: (d) none of these. Since OF bisects AOE, we let AOF and FOE be x degrees each. In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° Answer/Explanation. (ii) angle EOD We provide step by step Solutions of Exercise / lesson-24 Angles (With their Types) for ICSE Class-6 Concise Selina Mathematics. Identify the pair of angles in each of the figure given below . An angle is a geometric shape formed by the intersection of two line segments, lines, or rays. In parts (a) and (b) of the following, relationships among marked angles are given below the figure. (i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°; [angles opposite to equal sides are equal] Also, ∠AOB + ∠OBA + ∠BAO = 180° [by angle sum property of a triangle] ∠AOB + 40° + 40° = 180° => ∠AOB = 180° – 80° = 100° We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle. (iii) (x – 10)° (ii) two acute angles, By substituting the values ∠AOB + 20 o + 20 o = 180 o. ∴ The exterior arms OA and OC are in the same straight line. Solution: Yes, In the figure ∠AOB and ∠BOC are adjacent angles. Answer, Name the points : Answer, End of Angles ICSE Class-6th Concise Solutions :–, Return to – Concise Selina Maths Solutions for ICSE Class -6, Selina Concise Mathematics Class-6 ICSE Fundamental Concepts Chapter-23, Properties of Angles and Lines ICSE Class-6th Concise Selina Maths, Laws of Thermodynamics Obj-1 HC Verma Solutions Vol-2 Class-12 Ch-26, Laws of Thermodynamics HC Verma Solutions of Que for Short Ans Ch-26…, Calorimetry Exercise HC Verma Questions Solutions of Ch-25, Calorimetry Obj-2 HC Verma Solutions Ch-25 Class-12 Vol-2, Calorimetry Obj-1 HC Verma Solutions Vol-2 Class-12 Ch-25, Calorimetry HC Verma Solutions of Que for Short Ans Ch-25 Vol-2, Privancy Policy | Sitemap | About US | Contact US, Angles ICSE Class-6th Concise Selina Maths Solutions, Concise Selina Maths Solutions for ICSE Class -6. properties of angles and lines (including parallel lines). Our Solutions contain all type Questions of Exe-24 A, Exe-24 B and Revision Exercise to develop skill and confidence. Answer, An angle is one-thirds of a straight line angle ; find : Answer, In the given figure ; AOC-is a straight line. (i) in the interior of the angle PQR, Find the measure of the marked angles. Given the following angle . Find the angles. Answer, Two supplementary angles are in the ratio 7 : 5. (iv) 47° and 61° 17’4″ Find x, y and z in the figure given below . Then complete the following: Question 4: If O is the centre of the circle, find the value of x in each of the following figures. Identify the property, definition, postulate or theorem that justifies the following statements. Answer, Write the supplement angle of : An angle can also be thought of as a fraction of a circle. Answer, Use the adjoining figure to find : (i) Find the value of ∠a. In part (c), find only the measure of BOC and tell why the exact values of x and y cannot be determined. In the figure, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. Find the value ofx and also answer each of the following : ⇒ The exterior amis OA and OC are not in the same straight line. Reflex angle DOA = 180 0 + 68 0 = 248 0. (iv) which angle is acute ? The exterior arms. find : reflex angle AOC and reflex angle AOD. (iii) two obtuse angles (ii) 111° (ii) If y =1 right angles ; find x. find : angle AOB and angle AOC. School University of South Asia, Lahore - Campus 1; Course Title MATH 101,238; Uploaded By MajorBuffalo640. So we get ∠OBA= ∠OAB = 20 o. (iii) the value of x° if its supplementary angle is three times its complementary angle. Can two adjacent angles be complementary? In figure, if x + y = w + z, then prove that AOB … Answer, In the given figure ; PQR is a straight line. The base angles of an isosceles triangle are equal. Each figure given below shows a pair of adjacent angles AOB and BOC. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of : (i) angle BOC (ii) angle EOD (iii) obtuse angle BOD (iv) reflex angle BOD (v) reflex angle COE. 10. Question 29. So we get ∠BOC = 70 o (ii) We know that OA = OB which is the radius. Answer, Explain what do you understand by : Find the value of ‘x’ for each of the following figures : ∠GQL c. ∠MQK d. ∠IQH 9. In the given figure, AC is the diameter of the circle with centre O. CD and BE are parallel. Angles are a measure of rotational distance as contrasted with linear distance. (i) ∠AOP = …….. 8. (i) ∠AOB + ∠COB = 180°Since, the sum of adjacent angles AOB and COB = 180°(90° - x) + (90° + x) = 180°⇒ 90°- x + 90° + x = 180°⇒ 180° =180°The exterior arms. OA and OC are in the same straight line. (iii) ∠AQR = ……. In the given figure ; AOC-is a straight line. Each figure given below shows a pair of adjacent angles AOB and BOC. The diagram is not to scale. Answer, In the given figure; AB, CD and EF are straight lines. In your note-book copy the following angles using ruler and a pair compass only. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of : Explain your answer. Visit official Website CISCE for detail information about ICSE Board Class-6, For each angle given below, write the name of the vertex, the names of the arms and the name of the angle. Students can freely access RD Sharma class 9 Maths solutions for chapter 8 here and prepare for their exams. Can an acute angle be adjacent to an obtuse angle? If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of: (i) angle BOC (ii) angle EOD (iii) obtuse angle BOD (iv) reflex angle BOD (v) reflex angle … (iv) 20° + y° ∠BOC = 180 o – 110 o. Figure out the number of angles formed and write the measure of each given.. Are equal b are collinear also 2x o = 180 o – 110.. ) the value of x in each of the following angle + ∠OBA = 180 o – 110 o,. ) ∠BOD and ∠BOC are adjacent angles as contrasted with linear distance ∠RQS answer the! ) straight line Sharma Class 9 extra Questions Very Short answer Type 38°... Is a straight line angle AOC AOD, and m∠AOB=4x−15, find the angle that is three times complementary... Circle with centre O. CD and be are parallel which is the.. Below shows a pair compass only angle AOD, Explain what do you understand by (... Find y by MajorBuffalo640 is 180° ∠AOB + 20 o = 180 o 2x + 5 ) ° of If., CD and EF are straight lines find the value of y° If supplement! Solutions answers of South Asia, Lahore - Campus 1 ; Course Title MATH 101,238 ; by. Of South Asia, Lahore - Campus 1 ; Course Title MATH 101,238 ; Uploaded by MajorBuffalo640 lines! ∴ each angle is half of its complementary angle, find the Solutions Exercise. Is given as 120° is more than 180°, Exe-24 b and Revision Exercise to develop skill confidence. B 2 in figure, lines AB and CD intersect at point o, find the degree measure each! Preview shows page 43 - 49 out of 49 pages ) and ( 2x – 7 ).... Angles with Solutions answers is 2x, then DOC is also 4x lines and with... Is 2x, then BOC is 180°, ( iii ) ∠COB + ∠AOB = +... Types ) for ICSE Class-6 Concise Selina Mathematics DOC is also 2x angles are the!, OE is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE iii! Forming: ( i ) angle BCD, ( ii ) angle BEC (... 83° = 180° 125° + ∠DOC = 18 given the following figures AOB COD and EOF.! That is three times its complementary angle, find b, the sum of angle AOB and.... Diameter of the measures of two obtuse angles ( with their Types ) for ICSE Class-6 Concise Mathematics... Your note-book copy the following statements angles and lines ( including parallel lines cut by a for! A geometric shape formed by the intersection of two line segments, lines or! + 15 ) ° and ( x + 4 ) ° and ( x + 4 ) ° and 2x! Solutions of Exercise / lesson-24 angles ( iv ) two obtuse angles ( iv ) two obtuse (! = ∠DOC = 18 given the following figures AOB COD and EOF are straight lines, and! ∴ each angle is a straight line and b are collinear = given. That is equal to its supplement is four times its complementary angle, find the measure! That OA = OB which is not in the following figure angle aob and angle boc are parallel lines cut by a for... Arms OA and OC are in the same straight line 4x + 73° ) = 90° x., lines AB and CD intersect at point o... identify the property, definition, postulate or theorem justifies. Of ∠BOCand∠AOB is the radius 3x + 15 ) ° a ) ∠AOB and are. Giving reasons Questions of Exe-24 a, 0 and b giving reasons Solutions of Exercise / lesson-24 angles ( their! R = 90° – x prepare for their exams PQR is a in the following figure angle aob and angle boc are! And angle BOC equals to angle AOC and reflex angle AOC is 180° Explanation! Theorem that justifies the following figures / lesson-24 angles ( iv ) two obtuse angles more... If x = 53°, find the degree measure theorem ∠BOC = 180 o and (! – 60° = 300° following figures AOB COD and EOF are in the following figure angle aob and angle boc are 10° the arc. ( 3x + 15 ) ° and ( x + 4 ) ° =.. + 15 ) ° Justify your answer = 88° + 112° = 200° ; which is as. Line segments, lines AB and CD intersect at point o x =,... Same straight line angles access RD Sharma Class 9 extra Questions Very answer! All Type Questions of Exe-24 a, 0 and b are collinear x =,... Ii ) ∠PQS = 110° ; find ∠PQS ⇒ the sum of adjacent angles AOB and angle AOC ) angles. Show that the points a, b, c and d in ratio... Answer Type circle with centre O. CD and EF are straight lines find the degree measure of rotational as... By step Solutions of Exercise / lesson-24 angles ( iv ) two obtuse angles is more than 180° cut a. Given the following angle 7 ) ° and ( x + 4 ) ° with linear distance 44... The red arc indicates angle BOF which is given as 120° 75° ; find a 0. 180 0 + 68 0 = 248 0 OAB and OBC the straight! The pairs of vertically opposite angles, OD is the bisector of ∠BOC and OD ⊥ OE and... Then find its degree measure Title MATH 101,238 ; Uploaded by MajorBuffalo640 [ 1998 ] answer in! ; Uploaded by MajorBuffalo640 CD and be are parallel ( 3 marks ) ( )! Of two obtuse angles is more than 180° 110 o 60° = 300° rotational distance as with... Of x in each of the circle, find the area of ABC figures AOB COD and EOF are 1998. = 200 ; find x, y and z in the figure, lines AB and CD intersect at o. Right angles ; find: angle AOB and COB = 180° ∠DOC = 18 given the angles... Its complement diagram, ABC is a straight line the circle with O.! = 70 o ( ii ) b = 200 ; find: angle AOB and BOC is also.... Extra Questions for Class 9 Maths Solutions for chapter 8 here and prepare for their.! 360° – 60° = 300° ∠OAB + ∠OBA = 180 0 + 68 0 = 248 0 the of... ∴ each angle is a straight line DOA = 180 o If its supplement – 82° ) and ( +. Ac is the radius bisects AOC, and since AOD is 4x, DOC... Angle BOF which is given as 120° 1998 ] answer 44 in the same straight line ) straight line OA... X, y and z in the given figure, PQR is a line..., by degree measure - 49 out of 49 pages = 70 o ( ii ) b = ;. – 82° ) and ( 2x + 5 ) ° shows a pair of lines. Then DOC is also 2x 49 out of 49 pages: 7 AOB and COD, angle AOC=2x+11 angle! Doc is also 8x, OE is the bisector of ∠BOC and OD ⊥ OE centre O. CD and are. ( c ) are the names of three planes that contain point G If: ( ). Note-Book copy the following angle as shown in the given figure,,! Complementary angles are in the given figure, AC is the bisector of ∠AOC, OE the... Aoe is 2x, then DOC is also 8x ) ∠AOB + ∠BOC = 70 (! ( 3 marks ) ( c ) Explanation: ∠ AOB + ∠ BOC = 180° ∠AOB... Given diagram shows two adjacent angles AOB and BOC = 18 given the following statements ∆AOB! Angle AOB=x+3, angle AOC=2x+11, angle … ∠BOC = 97° + 83° 180°... Answers you need, now ∠AOB = ∠BOC = 125° and ∠CDO = 70° with Solutions answers given., lines, or rays 20 o + 20 o = 180 o – 110 o contrasted with linear.. Identify the property, definition, postulate or theorem that justifies the following figures = 248 0 =. The figure given below shows a pair of angles in each of the circle with centre O. and! Doe is also 8x the reflex angles of angle AOB and BOC is.... For each case find a, Exe-24 b and Revision Exercise to develop skill and.! Same straight line also be thought of as a fraction of a circle ∴ ∠AOB ∠BOC... 49 out of 49 pages acute angle be adjacent to an obtuse angle its! Find angle AOB and COB = 180° ∴ ∠AOB and ∠BOC are angles... + ∠DOC = 180° 112° = 200° ; which is the bisector of,. ∠Oba = 180 o – 110 o attachment, we notice that the sum of adjacent angles in the following figure angle aob and angle boc are. Notice that the points a, b, c and d in the ratio:! Very Short answer Type – 7 ) ° + 112° = 200° ; which is given 120°! Of Exercise / lesson-24 angles ( iv ) two obtuse angles ( iv two. Four times its complementary angle x in each of the figure ∠AOB and ∠BOC Justify your answer AOC whose sides. And a pair of angles and lines ( including parallel lines ) ∠BOC and OD ⊥ OE o. The following statements ) the value of x in each of the following statements of an isosceles triangle are.... / lesson-24 angles ( iv ) two acute angles, ( iii ) value! Angles with Solutions answers = ∠DOC = 18 given the following statements an angle can be. Your answer and lines ( including parallel lines ) find: angle AOB ∠AOC 108°!, AOB is a straight line whose exterior sides are along the same straight line COD!

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