Question

In fig. 6.39, side QP and RQ of ΔPQR are produced to points S and T respectively, if ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.

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Answer 1

PRQ = 65 degrees

Explanation:

Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).

SPR + QPR = 180

135 + QPR = 180

QPR = 45

TQP + RQP = 180

110 + RQP = 180

RQP = 70

Since interior angles of a triangle add up to 180 ...

QPR + RQP + PRQ = 180

45 + 70 + PRQ = 180

PRQ = 65