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

Question

Philoid · Accepted Answer

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.

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