Mathematics

Problem

In a cyclic quadrilateral

WXYZ

, the measures of the four interior angles are represented by

\angle W=(2x+15)^\circ,\; \angle X=(3y-5)^\circ,\; \angle Y=(5x-25)^\circ

and

\angle Z=(4y+5)^\circ

. a. (i) Write the two equations that arise from the property of opposite angles in a cyclic quadrilateral. b. (ii) Solve the simultaneous equations to obtain the values of

x

and

y

. c. (iii) Hence calculate the measures of

\angle W,\; \angle X,\; \angle Y

and

\angle Z

. d. (iv) Verify that each pair of opposite angles adds up to

180^\circ

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