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Answer 1

Given:- A triangle ∆PQR in which PQ = PS . Value of ∠SRP = 25° . Also x = ∠SPR .

To Find:- The value of x and y .

Answer :-

Now here in ∆PSQ , PQ = PS . So , ∠PQS = ∠PSQ ( since sides opposite to equal angles are equal ) .

Hence , ∠ PSQ = ∠PQS = y .

Also , here TR is a straight line . So , its angle will be 180° .

=> 110° + y = 180° .

=> y = 180° - 110° .

→ y = 70° .

★Hence the value of y is 70° .

$\rule{200}2$

Now , again in ∆PSR ;

=> ∠SPR + ∠PRS = ∠PSQ . [ By Exterior angle property ]

=> x + 25° = y.

=> x + 25° = 70° .

=> x = 70° -25°

→ x = 45°

★ Hence the value of x is 45° .

Hence the value of x is 45° and that of y is 70° .