Mathematics

Problem

In a quadrilateral

ABCD

inscribed in a circle, the measures of two opposite angles are given by

\angle A = 3x + 15^\circ

and

\angle C = 5x - 25^\circ

. a. (i) Find the value of

x

. b. (ii) Hence calculate the numerical values of

\angle A

and

\angle C

. c. (iii) If

\angle B : \angle D = 4 : 5

, determine the measures of

\angle B

and

\angle D