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