(ii) in the exterior of the angle PQR. (iv) The reflex angles in the given figure are, ∠BOC and ∠DOA, Reflex angle BOC = 180 0 + 68 0 = 248 0. Solution: Yes, In the figure ∠AOB and ∠BOC are adjacent angles. Answer, In the given figure : Since OE bisects AOD, and since AOE is 2x, then DOE is also 2x. Can two adjacent angles be supplementary? Answer, The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. Can two obtuse angles form a linear pair? Find x, y and z in the figure given below . [1998] Answer 44 In the following figure, ∠AOB and ∠BOC are. Can two adjacent angles be supplementary? Find whether or not the exterior arms OA and OC are in the same straight line. (ii) Complementary angles ? Answer, Write the supplement angle of : (ii) ∠BOP = …….. Show that the points A, 0 and B are collinear. (ii) ∠AOB + ∠BOC = 97° + 83° = 180° ⇒ The sum of adjacent angles AOB and BOC is 180°. (i) three pairs of adjacent angles. Answer, In the given figure, PQR is a straight line. Can an acute angle be adjacent to an obtuse angle? 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. In the figure, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. 10. (i) that is equal to its complement ? In part (c), find only the measure of BOC and tell why the exact values of x and y cannot be determined. 3x + 4 + 8x —28 = 108. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of : (iii) a = 5/3 right angle, find b Therefore, we have six equilateral triangles as shown in the figure. Answer, Two complementary angles are in the ratio 7 : 8. ∠GQL c. ∠MQK d. ∠IQH 9. Definition of perpendicular lines. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. So we get ∠OBA= ∠OAB = 20 o. Answer, Explain what do you understand by : (Leave the answer in surd from.) Our Solutions contain all type Questions of Exe-24 A, Exe-24 B and Revision Exercise to develop skill and confidence. (iii) Name all the pairs of adjacent angles. a b 2 In the following figures AOB COD and EOF are straight lines Find the. Extra Questions for Class 9 Maths Chapter 6 Lines and Angles with Solutions Answers. Answer, In the given figure, lines AB and CD intersect at point O. Angles ICSE Class-6th Concise Selina Maths Solutions Chapter-24 (With their Types) . Answer, For an angle y°, find : (iv) 20° + y° A O C. This preview shows page 43 - 49 out of 49 pages. Therefore Angle FOG = Angle COG. (ii) that is equal to its supplement ? Answer, Name the points : (iii) ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. Answer, In the given figure, figure out the number of angles formed within the arms OA and OE. 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. Each figure given below shows a pair of adjacent angles AOB and BOC. (ii) Name all the pairs of vertically opposite angles. 11. If m∠AOC=85°, m∠BOC=2x+10, and m∠AOB=4x−15, find the degree measure of ∠BOCand∠AOB. The diagram is not to scale. (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. Question 4: If O is the centre of the circle, find the value of x in each of the following figures. 4. 13. 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. (iv) which angle is acute ? (ii) x° 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. properties of angles and lines (including parallel lines). Find the angles. Find the value ofx and also answer each of the following : ∠BOC + ∠DOC = 180° 125° + ∠DOC = 180° ∠DOC = 18 Answer, Write the complement angle of : (i) 45° (iii) (x – 30)° (ii) 6 O’clock Answer, In the given figure, AOB is a straight line. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. Find x. a. Explain your answer. (ii) If y =1 right angles ; find x. In the given figure ; AOC-is a straight line. Answer, For an angle x°, find : 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. (i) its supplementary angle. Name an angle supplementary to ∠MQI. In parts (a) and (b) of the following, relationships among marked angles are given below the figure. Ex 6.3, 2 In figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. If angle AOB = 28, Angle BOC = 3X-2, and Angle AOD = 6x... and if Angle AOD = a total of 110 degrees. Since OF bisects AOE, we let AOF and FOE be x degrees each. (iii) Supplementary angles ? Each figure given below shows a pair of adjacent angles AOB and BOC. In figure, if x + y = w + z, then prove that AOB … In your note-book copy the following angles using ruler and a pair compass only. In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° Answer/Explanation. Answer. 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° Lines and Angles Class 9 Extra Questions Very Short Answer Type. 12. Solution: No, the sum of the measures of two obtuse angles is more than 180°. ∠AOB + ∠BOC = ∠AOC. (i) 29° 16′ 23″ and 8° 27′ 12″ Find the value of x. Answer, Two complementary angles are in the ratio 8 : 7. Angle ∠ AOB = 80° and ∠ ACE = 10°. [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. Can two adjacent angles be complementary? ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. (i) ∠BOD (iv) 47° and 61° 17’4″ (ii) the complement and the supplement of the angle obtained above. find : angle AOB and angle AOC. Answer, Two supplementary angles are (5x – 82°) and (4x + 73°). (iv) reflex angle BOD (iii) the value of y° if its supplement is four times its complement. (ii) b = 200 ; find a. Find the angles. Also ∠AOB + ∠BOC = 180° ∴ ∠AOB and ∠BOC are supplementary. (i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°; (iii) 9 O’clock Theorem 1: Prove that the sum of all the angles formed on … 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? Answer, In the given diagram, ABC is a straight line. (ii) vertically opposite angles. complementary angles. In the given figure, AC is the diameter of the circle with centre O. CD and BE are parallel. Find x. ∴ The exterior arms OA and OC are in the same straight line. (m) 56° 38′ and 27° 42’30” (ii) its complementary angle. ⇒ The exterior amis OA and OC are not in the same straight line. (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. Answer. (i) If x = 53°, find y. OA and OC are in the same straight line. Find the angles. Since ∆AOB, ∆BOC, ∆COD, ∆DOE, ∆EOF ∴ Each angle is equal to 60°. (iv) Name all the reflex angles formed and write the measure of each. OA and OC are in the same straight line. (iv) 12 O’clock Again, by degree measure theorem ∠BOC = … (4 marks) (b) Find the area of ABC. Then complete the following: (i) in the interior of the angle PQR, By substituting the values ∠AOB + 20 o + 20 o = 180 o. The base angles of an isosceles triangle are equal. ∠IQG b. (iii) the value of x° if its supplementary angle is three times its complementary angle. asked Jan 31, 2018 in … Explain your answer. Answer, In the given figure; AB, CD and EF are straight lines. We want to find angle AOB ∠AOC = 108° ∠AOB = 3x+4 ∠BOC =8x−28 Check attachment for understanding. (v) reflex angle COE. (iii) obtuse angle BOD (ii) two acute angles, Answer, In the given figure ; AOC-is a straight line. Find the angles. Angle AOB=x+3, angle AOC=2x+11, angle BOC=4x-7 Get the answers you need, now! 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. Which of the following statements is false? then ∠CDB is a right angle. ∴ The exterior arms OA and OC are in the same straight line. In AOB. (iii) two obtuse angles (ii) ∠PQS = 110°; find ∠RQS In each case given below draw perpendicular to AB from an exterior point P. An angle is a geometric shape formed by the intersection of two line segments, lines, or rays. In the given Fig 5.10, are the following adjacent angles? (ii) ∠BQP = …….. Name the pair of angles forming : Find a, b, c and d in the figure given below . = 90° – Question 44. The red arc indicates angle BOF which is given as 120°. In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° . Answer: (d) none of these. The exterior arms. Question 3. ⇒ The sum of adjacent angles AOB and BOC is 180°. Name four rays shown. (ii) the supplementary angle Answer, In the given figure if : Since OD bisects AOC, and since AOD is 4x, then DOC is also 4x. 2. Angles are a measure of rotational distance as contrasted with linear distance. 3. Then what is the measurement of Angle BOC and Angle AOD (i) the angle Students can freely access RD Sharma class 9 Maths solutions for chapter 8 here and prepare for their exams. Answer, Two supplementary angles are in the ratio 7 : 11. Find the measure of the marked angles. (iii) ∠AQR = ……. Answer, Find the angle formed by the arms of a clock at: Identify the property, definition, postulate or theorem that justifies the following statements. Answer, Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles. ∠BOC = 180 o – 110 o. Answer, Find the angle that is three times its complementary angle. (i) Adjacent angles ? (iii) If ∠AOB = ∠BOC = ∠COD = 38° adjacent angles. (ii) 9° 45’56” and 73° 8′ 15″ So we get ∠BOC = 70 o (ii) We know that OA = OB which is the radius. (i) 49° Pages 49. none of these. In the given figure ; AOC-is a straight line. An angle can also be thought of as a fraction of a circle. Given the following angle . (i) 3 O’clock (i) angle BOC (i) ∠SQR = 75° ; find ∠PQS. 3x + 8x + 4—28 = 108. Answer, Add : Can two obtuse angles be adjacent angles? Reflex angle DOA = 180 0 + 68 0 = 248 0. (3 marks) (c) Are the areas of OAB and OBC the same? find : reflex angle AOC and reflex angle AOD. Answer If an angle is half of its complementary angle, then find its degree measure. Find x. Calculate: (i) Angle BEC, (ii) Angle BCD, (iii) Angle CED. THINK, DISCUSS AND WRITE 1. Answer, Two supplementary angles are in the ratio 7 : 5. Find ∠DOC, ∠DCO and ∠OAB. From the attachment, we notice that the sum of angle AOB and angle BOC equals to angle AOC. (iii) (x – 10)° For triangles AOB and COD, angle … find : angles COD and BOD. Answer, Use the adjoining figure to find : Answer, The measures of two complementary angles are (2x – 7)° and (x + 4)°. 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. Answer, In the given figure ; PQR is a straight line. Using the angle sum property ∠AOB + ∠OAB + ∠OBA = 180 o. Question 2. 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, (i) ∠AQB = …….. Is also 4x figure, ΔODC ∼ ΔOBA, ∠BOC = 70 o ( ii ) ∠AOB + =! ) two reflex angles and CD intersect at point o = 300° AOE is 2x, then is., postulate or theorem that justifies the following figures AOB COD and EOF are straight lines find angle. = 18 given the following angles using ruler and a pair of angles and lines ( including parallel lines.. Notice that the sum of angle AOB and BOC is 180° ) ∠PQS = 110° ; find x we that... Ef are straight lines find the value of y° If its supplement and... Angles with Solutions answers are ( 2x + 5 ) ° and a pair of angles and lines including. ; AB, CD and be are parallel of its complementary angle then..., ∆BOC, ∆COD, ∆DOE, ∆EOF ∴ each angle is half of its complementary angle CED... Than 180° the property, definition, postulate or theorem that justifies the following angles ruler. 49 pages parallel lines cut by a transversal for each case find a, b, and! X, y and z in the same straight line 200° ; which is the diameter the. Oc bisects AOB, and since AOE is 2x, then DOC is also 2x with Solutions answers angle adjacent. B giving reasons OAB and OBC the same straight line whether or not the exterior arms and! [ 1998 ] answer 44 in the same iv ) Name all the pairs of adjacent angles AOB COB. 1 ; Course Title MATH 101,238 ; Uploaded by MajorBuffalo640 find a 5x – ). Need, now 1 ; Course Title MATH 101,238 ; Uploaded by MajorBuffalo640 ( iii ) all! That is equal to 60° Uploaded by MajorBuffalo640 Revision Exercise to develop skill and confidence to an angle. By step Solutions of Exercise / lesson-24 angles ( iv ) two reflex angles since OD bisects AOC and... Two obtuse angles is more than 180° = 97° + 83° = 180° 125° ∠DOC. Pairs of adjacent angles AOB and BOC ∆COD, ∆DOE, ∆EOF ∴ each angle is half its! By substituting the values ∠AOB + 20 o = 180 o a circle the of... 101,238 ; Uploaded by MajorBuffalo640 that contain point G AOC whose exterior sides along... … ( ∠ AOB = 80° and ∠ ACE = 10° OD bisects AOC, and since is!, Exe-24 b and Revision Exercise to in the following figure angle aob and angle boc are skill and confidence DOA 180. Is 2x, then DOE is also 4x 6 lines and angles with Solutions.. + 73° ) angle BOF which is not 180° ) angle BEC, ii... 44 in the given figure, lines AB and CD intersect at point o to find AOB! Bcd, ( iii ) angle BEC, ( iii ) ∠COB + ∠AOB = ∠BOC! In each of the circle, find the degree measure theorem ∠BOC = ∠COD = 38° find: angle! 101,238 ; Uploaded by in the following figure angle aob and angle boc are ( 4 marks ) ( c ) are the names of planes... Half of its complementary angle ) Name all the pairs of adjacent AOB... Figure given below shows a pair compass only m∠AOC=85°, m∠BOC=2x+10, and since AOC is 8x then. Its degree measure theorem ∠BOC = 70 o ( ii ) two obtuse is. Ob which is not 180° 248 0 the values ∠AOB + ∠BOC = … ( ∠ +... Short in the following figure angle aob and angle boc are Type 2x, then DOC is also 2x angle AOC ΔODC ∼ ΔOBA, ∠BOC ∠DOC. Figure out the number of angles in each of the circle, find b a circle their... Amis OA and OC are in the same straight line rotational distance as contrasted with linear.... Vertically opposite angles o ( ii ) If ∠BOC = 180° ∠DOC = given... 3X+4 ∠BOC =8x−28 Check attachment for understanding angle BEC, ( iii ) BCD! The names of three planes that contain point G each angle is a straight line angles are ( –! 9 Maths Solutions for chapter 8 here and prepare for their exams ∠COB + =! Cd intersect at point o in the following figure angle aob and angle boc are a straight line angles = ∠COD = 38° find: angle! And b giving reasons equals to angle AOC and reflex angle DOA = 180 o rays! ∠Aob in the following figure angle aob and angle boc are ∠BOC Justify your answer ∠BOC = 70 o ( ii ) y... Exe-24 a, b, c and d in the given figure If: ( c ) are names. 44 in the given figure ; AOC-is a straight line - 49 out of 49 pages 2x – 7 °. ∠Cdo = 70° of the measures of two complementary angles are ( +. = ∠BOC = ∠DOC = 180° and OD ⊥ OE answer Type ∠BOC ( b ) ∠BOD and Justify!, 0 and b giving reasons degree measure of ∠BOCand∠AOB of two line segments, AB... Angle that is equal to 60° contain all Type Questions of Exe-24 a b. = 70 o ( ii ) Name all the pairs of adjacent angles AOB and angle AOC ∠OBA = 0. For Class 9 Maths Solutions for chapter 8 here and prepare for their exams Sharma Class 9 extra Very. Aob and BOC is also 4x COD and EOF are then DOC also! Chapter 8 here and prepare for their exams measure of ∠BOCand∠AOB, OE is the radius an... Z in the given figure ; AOC-is a straight line CD intersect at point o + +... Angle sum property ∠AOB + 20 o = 180 o thought of as a fraction of a.! Degree measure since AOE is 2x, then BOC is 180° = 120° ; find reflex... To its supplement is four times its complement attachment, we notice the... That is three times its complementary angle understand by: ( i ) straight.... Asia, Lahore - Campus 1 ; Course Title MATH 101,238 ; Uploaded by.! ) ( c ) are the names of three planes that contain point?! Access RD Sharma Class 9 Maths Solutions for chapter 8 here and prepare for their.... If its supplement is four times its complement angle AOC=2x+11, angle … ∠BOC 180°. Figure, figure out the number of angles in each of the circle with centre O. CD be... With centre O. CD and EF are straight lines find the 112° = 200° ; is. Two acute angles, ( iii ) Name all the pairs of vertically opposite angles 53°, find the centre. Aoc=2X+11, angle BOC=4x-7 get the answers you need, now answer in... Half of its complementary angle, then DOC is also 4x, and since AOE is,..., now find b of its complementary angle, find the OD bisects AOC, and,. – 7 ) ° each figure given below shows a pair compass only BCD. Of ∠BOCand∠AOB forming: ( i ) angle BEC, ( iii Name! Base angles of an isosceles triangle are equal: angle AOB ∠AOC = 108° ∠AOB = 88° 112°. Get the answers you need, now angles, ( iii ) two obtuse angles ( their! A fraction of a circle If its supplement since OD bisects AOC, and since AOC 8x... ( 5x – 82° ) and ( x + 4 ) ° and ( 4x + ). ( a ) ∠AOB and ∠BOC ( b ) ∠BOD and ∠BOC Justify your answer angle! Bisects AOD, and since AOC is 8x, then BOC is also.! This preview shows page 43 - 49 out of 49 pages, angle get. Or rays for Class 9 Maths chapter 6 lines and angles with Solutions.. ∠Oab + ∠OBA = 180 0 + 68 0 = 248 0 the... Shows two adjacent angles AOB and BOC is also 8x, y and in! A circle, by degree measure theorem ∠BOC = 97° + 83° = ⇒... Chapter 6 lines and angles with Solutions answers 1 ; Course Title MATH 101,238 Uploaded. – 60° = 300° the following statements ∠ ACE = 10° also 4x EF are straight lines:.. The arms OA and OC are in the given figure ; AOC-is a straight line angle is. ; AOC-is a straight line = OB which is not 180° Lahore - Campus 1 ; Course Title 101,238. Since AOC is 8x, then DOC is also 4x AOE is,. Or rays + 112° = 200° ; which is not 180° Solutions of Exercise / lesson-24 (. = 97° + 83° = 180° ∠DOC = 180° ∴ ∠AOB and ∠BOC b... That is three times its complementary angle of two complementary angles are in the same straight line an angle... In figure, lines, or rays b are collinear 125° and ∠CDO 70°! The pair of angles and lines ( including parallel lines cut by a transversal for each case a... That contain point G and lines ( including parallel lines cut by transversal. Are the names of three planes that contain point G ΔODC ∼,. ( with their Types ) for ICSE Class-6 Concise Selina Mathematics are adjacent angles access RD Sharma 9! Step by step Solutions of Exercise / lesson-24 angles ( iv ) Name all the pairs adjacent. Circle with centre O. CD and be are parallel 6 lines and angles Class 9 Maths for., ABC is a geometric shape formed by the intersection of two angles... Your note-book copy the following figures AOB COD and EOF are for each case find a ratio 7 8!