Mathematics
In Fig. ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.
Lines & Angles
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Answer
Given,
⇒ ∠PQR = ∠PRQ = x (let)
From figure,
⇒ ∠PQS + ∠PQR = 180° (Linear pair)
⇒ ∠PQS = 180° - ∠PQR
⇒ ∠PQS = 180° - x …….(1)
From figure,
⇒ ∠PRT + ∠PRQ = 180°
⇒ ∠PRT = 180° - ∠PRQ
⇒ ∠PRT = 180° - x ………(2)
From equations, (1) and (2) we get :
⇒ ∠PQS = ∠PRT
Hence, proved ∠PQS = ∠PRT.
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