Q. 34.0( 12 Votes )

In Fig. 6.7, PQ = PS. The value of x is


A. 35°

B. 45°

C. 55°

D. 70°

Answer :

Given: In ΔPQS


PQ = PS, Exterior angle with Q is 110°


In ΔPSR


PRS = 25°, RPS = x


Formula Used/Theory:-


Exterior angle of triangle is equal to sum of 2 opposite interior angles .


As RQ is straight line


PQS + 110° = 180°


PQS = 180° - 110°


PQS = 70°


As ΔPQS is isosceles triangle and PQ = PS


PQS = PSQ


PSQ = 70°


In ΔPSR


With exterior angle PSQ equal to sum of opposite interior angles


PSQ = SPR + PRS


70° = x + 25°


x = 70° - 25°


x = 45°

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