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Question
In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135º and ∠PQT = 110º, find ∠PRQ.
Solution
It is given that,
∠SPR = 135º and ∠PQT = 110º
∠SPR + ∠QPR = 180º (Linear pair angles)
⇒ 135º + ∠QPR = 180º
⇒ ∠QPR = 45º
Also, ∠PQT + ∠PQR = 180º (Linear pair angles)
⇒ 110º + ∠PQR = 180º
⇒ ∠PQR = 70º
As the sum of all interior angles of a triangle is 180º, therefore, for ΔPQR,
∠QPR + ∠PQR + ∠PRQ = 180º
⇒ 45º + 70º + ∠PRQ = 180º
⇒ ∠PRQ = 180º − 115º
⇒ ∠PRQ = 65º
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