Mathematics

Mathematics

Problem

Points

A, B, C

and

D

lie on a circle. The chord

AB

subtends

\angle ACB = 40^{\circ}

at point

C

and

\angle ADB = 4x - 20^{\circ}

at point

D

on the same side of

AB

. The chord

AC

subtends

\angle ABC = 3x + 5^{\circ}

at point

B

. a. (i) Find the value of

x

. b. (ii) Calculate

\angle ADB

and

\angle ABC

. c. (iii) Hence, determine the measure of

\angle ADC

.

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