In a circle, chord subtends angles at two points and on the same segment such that…

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

In a circle, chord

MN

subtends angles at two points

A

and

B

on the same segment such that

\angle MAN = (3x + 10)^\circ \quad \text{and} \quad \angle MBN = (5x - 26)^\circ.

Answer the following. (i) Find the value of

x

. (ii) Hence determine the measures of

\angle MAN

and

\angle MBN

. (iii) If

\angle MON

is the angle subtended by the same chord

MN

at the centre

O

, calculate

\angle MON