Question

In triangle QSR sides SQ and RS are produced to points T and P respectively, ZTQR = 105°
and ZPSQ = 100° find ZSRQ.​

Answer 1

Given : In triangle QSR sides SQ and RS are produced to points T and P respectively, ∠TQR = 105°  and ∠PSQ = 100°  

To Find : ∠SRQ

Solution:

Exterior angle of triangle = Sum of opposite interior angles

=> ∠TQR =  ∠QSR  + ∠SRQ

   ∠PSQ = ∠SQR  + ∠SRQ

Adding both

=> ∠TQR +   ∠PSQ = ∠QSR  + ∠SRQ + ∠SQR  + ∠SRQ

=> 105° + 100° = (∠QSR  + ∠SRQ + ∠SQR)  + ∠SRQ

Sum of angle sof triangles = 180° ( Δ QSR)

=> 205° =  180° + ∠SRQ

=> ∠SRQ  = 25°

∠SRQ  = 25°  

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