Question

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

Answer 1

The measure of minor arc NQ in circle P, where the inscribed angle ∡NRQ is 60°, is 120°. This is found by doubling the measure of the inscribed angle, because the inscribed angle is half of the intercepted arc.

Step-by-step explanation:

The student is asking about circle geometry, specifically about calculating the measure of a minor arc when given the measure of an inscribed angle. In accordance with the relationship that the inscribed angle is half of the intercepted arc, if the measure of ∡NRQ is given as 60°, then the measure of the minor arc NQ is simply double that of the inscribed angle, which would be 120°.

To find the measure of the minor arc NQ, we apply the following steps:

1. Identify the inscribed angle (∡NRQ) and its measure, which is 60°.
2. Remember the rule that the inscribed angle is half of the intercepted arc. In this case, since ∡NRQ is the inscribed angle, it is half of the measure of arc NQ.
3. Therefore, to find the measure of arc NQ, we multiply the given angle measure by 2. The calculation is as follows: 2 × 60° = 120°.

Thus, the measure of the minor arc NQ is 120°.

Answer 2

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 =(1)/(2) m(ar NQ)`

Multiply by 2 on both sides.

`$\Rightarrow 2 * m\angle NRQ =2 * (1)/(2) m(ar NQ)`

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

Substitute m∠NRQ = 60°.

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

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

The measure of minor arc NQ is 120°.