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