Question

Please solve the question.

Answer 1

a = 125°, b = 20°, c = 35°, d = 90°, e = 55°

Explanation:

Quadrilateral PQRS is inscribed in a circle, therefore it is a cyclic quadrilateral.

PQ is diameter, SR is chord and PR is transversal such that:

PQ || SR... (given)

`m\angle PRQ = 90°..(\angle \: inscribed \: in\: semicircle) \\</p><p>\huge \red {\boxed {\therefore d = 90°}} \\\\</p><p>m\angle RPQ= m\angle PRS .. (alternate \: \angle s) \\</p><p>\huge \purple {\boxed {\therefore c = 35°}} \\\\</p><p>In\: \triangle PQR, \\</p><p>c + d + e = 180°\\</p><p>35° + 90° + e = 180°\\</p><p>125° + e = 180°\\</p><p>e = 180° - 125°\\</p><p>\huge \orange {\boxed {\therefore e = 55°}} \\\\</p><p>a + e = 180°...(opposite \:\angle 's \: of \: cyclic \: quadrilateral) \\</p><p>a + 55°= 180°\\</p><p>a = 180°- 55°\\</p><p>\huge \blue {\boxed {a = 125°}} \\\\</p><p>In\: \triangle PSR, \\</p><p>a + b + 35°= 180°\\</p><p>125° + b + 35° = 180°\\</p><p>160° + b = 180°\\</p><p>b = 180° - 160°\\</p><p>\huge \pink {\boxed {b = 20°}} </p><p>`