In the given figure if PQR is an isosceles triangle and PSR is an equilateral triangle and x = 26° then the value of y(in degrees) will be

The correct answer is (c) 17°.

In an isosceles triangle, the angles opposite the congruent sides are congruent. Therefore, $\angle P = \angle Q = 180^\circ – 2x = 90^\circ – x$.

In an equilateral triangle, all three angles are congruent. Therefore, $\angle S = \angle R = 60^\circ$.

Since $\angle PQR$ and $\angle PSR$ are supplementary angles, $y + 17 + 17 = 180^\circ$. Therefore, $y = 17^\circ$.