Quadrilateral is inscribed in a circle with

MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles

Problem

Quadrilateral

ABCD

is inscribed in a circle with

AB \parallel CD

. The measures of two opposite angles are

\angle A = (5x + 5)^\circ

and

\angle C = (3x + 25)^\circ

. (i) Write an equation in

x

that links

\angle A

and

\angle C

. (ii) Solve the equation to find the value of

x

. (iii) Hence determine the numerical values of

\angle A

and

\angle C

. (iv) Using the fact that

AB \parallel CD

, calculate

\angle B

and

\angle D

. (v) Verify that all four angles you have obtained satisfy the necessary conditions for a quadrilateral inscribed in a circle.