"Othello" written by William Shakespeare play explores themes of jealousy, manipulation, betrayal

Mathematics: Lines and Angles | Class: 9 | Chapter: 6 | Introduction | Theorem: 6.1 | Sums: 1 to 3

Introduction: Lines and Angles 

Theorem: 6.1

Sum: 1

Question 1:

In the given figure, lines AB and CD intersect at O. If and  find ∠BOE and reflex ∠COE.

ANSWER:

Sum: 2

Question 2:

In the given figure, lines XY and MN intersect at O. If ∠POY =  and a:b = 2 : 3, find c.

ANSWER:

Let the common ratio between a and b be x.

∴ a = 2x, and b = 3x

XY is a straight line, rays OM and OP stand on it.

∴ ∠XOM + ∠MOP + ∠POY = 180º

b + a + ∠POY = 180º

3x + 2x + 90º = 180º

5x = 90º

x = 18º

a = 2x = 2 × 18 = 36º

b = 3x= 3 ×18 = 54º

MN is a straight line. Ray OX stands on it.

∴ b + c = 180º (Linear Pair)

54º + c = 180º

c = 180º − 54º = 126º

∴ c = 126º

Sum: 3

Question 3:

In the given figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

ANSWER:

In the given figure, ST is a straight line and ray QP stands on it.∴ ∠PQS + ∠PQR = 180º (Linear Pair)∠PQR = 180º − ∠PQS (1)∠PRT + ∠PRQ = 180º (Linear Pair)∠PRQ = 180º − ∠PRT (2)It is given that ∠PQR = ∠PRQ.Equating equations (1) and (2), we obtain180º − ∠PQS = 180  − ∠PRT∠PQS = ∠PRT