Q. 234.8( 4 Votes )

In Fig. 6.12, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is


A. 55°

B. 40°

C. 50°

D. 45°

Answer :

Given: PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°


Formula Used/Theory:-


Base angle are equal is isosceles triangle


Alternate angles are equal if lines are parallel


Exterior angle is equal to sum opposite interior angles


In ΔPQR


UPR is exterior angle


UPR = Q + R


As ΔQPR is isosceles triangle because PQ = PR


Hence;


Q = R


140° = Q + R


2Q = 140°


Q = = 70°


As ΔQRS is isosceles triangle because QR = RS


Q = QSR


QSR = 70°


Then;


Q + QSR + SRQ = 180°


70° + 70° + SRQ = 180°


SRQ = 180° - 140° = 40°


As ST || QR


And SR is transverse


SRQ = TSR Alternate interior angles.


TSR = 40°

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