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
2∠Q = 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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