Q5 of 12 Page 84

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

In the figure, ST is a straight line and its angle is 180°


So, ∠PQS + ∠PQR = 180° ----(1)


And ∠PRT + ∠PRQ = 180°-----(2)


From the two equations, we get


∠PQS + ∠PQR = ∠PRT + ∠PRQ


Given that,


∠PQR = ∠PRQ


⇒ ∠PQS + ∠PRQ = ∠PRT + ∠PRQ


⇒ ∠PQS = ∠PRT + ∠PRQ -∠PRQ


⇒ ∠PQS = ∠PRT


So, ∠PQS = ∠PRT is proved.


More from this chapter

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In the given figure lines and intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

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