Question

Please solve the question.

Answer 1

Answer:

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

Step-by-step 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)

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