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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.

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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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