Question

In circle O, m∠R = 30.8°. Find m∠NOQ.

Answer 1

Given:

In circle O, m∠R = 30.8°.

To find:

The m∠NOQ

Solution:

Central angle theorem: According to this theorem, the central angle is always twice of subtended angle on the same arc.

Angle NOQ and angle NRQ are on the same arc but ∠NOQ is the central angle and ∠NRQ is the subtended angle on the arc NQ.

Using central angle theorem, we get

$m\angle NOQ=2\times m\angle NRQ$

$m\angle NOQ=2\times m\angle R$

$m\angle NOQ=2\times 30.8^\circ$

$m\angle NOQ=61.6^\circ$

Therefore, $m\angle NOQ=61.6^\circ$.