Quadrilateral is cyclic

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

Quadrilateral

ABCD

is cyclic. The measures of its angles are given by

\angle A=(3x+7)^\circ,\;\angle B=(2y+13)^\circ,\;\angle C=(4x-17)^\circ

and

\angle D=(5y-23)^\circ

. (i) Using an appropriate property of a cyclic quadrilateral, obtain two linear equations connecting

x

and

y

. (ii) Solve the simultaneous equations to find the values of

x

and

y

. (iii) Determine the numerical measures of all four angles of the quadrilateral. (iv) State whether

\angle A

is acute, right or obtuse, justifying your answer.