Mathematics

Mathematics

Problem

In a circle, chord

MN

subtends angles at two points

P

and

Q

on the same side of the chord. It is given that

\angle MPN = 3x + 15^{\circ}

and

\angle MQN = 5x - 25^{\circ}

. a. (i) Determine the value of

x

. b. (ii) Calculate the measures of

\angle MPN

and

\angle MQN

. c. (iii) If

O

is the centre of the circle, find

\angle MON

.

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