Question

In circle P with mNRQ = 60°, find the angle measure of minor arc NQ

Answer 1

Given:

m∠NRQ = 60°

To find:

The angle measure of minor arc NQ

Solution:

The inscribed angle is half of the intercepted arc.

$\Rightarrow m\angle NRQ =\frac{1}{2} m(ar NQ)$

Multiply by 2 on both sides.

$\Rightarrow 2 \times m\angle NRQ =2 \times \frac{1}{2} m(ar NQ)$

$\Rightarrow 2 \ m\angle NRQ =m(ar NQ)$

Substitute m∠NRQ = 60°.

$\Rightarrow 2\times 60^\circ=m(ar NQ)$

$\Rightarrow 120^\circ=m(ar NQ)$

The measure of minor arc NQ is 120°.