Mathematics

Problem

ABCD

is a cyclic quadrilateral. The interior angles are expressed as follows:

\angle A=(3x+5)^\circ,\;\angle C=(5x-25)^\circ,\;\angle B=(4y-7)^\circ

and

\angle D=(2y+13)^\circ

. a. (i) Using the properties of a cyclic quadrilateral, form an equation in

x

and hence find the values of

x

\angle A

and

\angle C

. b. (ii) Similarly, form an equation in

y

and determine

y

\angle B

and

\angle D

. c. (iii) List all four interior angles of

ABCD

after finding

x

and

y

. Verify that the opposite angles are supplementary.