Question

What is the measure of NQ?

Answer 1

Given:

Given that K is the center of the circle.

The measure of ∠NLQ is 44°

The measure of arc MP is 60°

We need to determine the measure of arc NQ

Measure of arc NQ:

Let us apply the property that, "if the measure of an angle formed by two secants drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs".

Thus, we have;

`\angle NLQ= \frac{\widehat{NQ} - \widehat{MP}}{2}`

Substituting the values, we have;

`44^(\circ)=\frac{\widehat{NQ}-60^(\circ)}{2}`

`88^(\circ)=\widehat{NQ}-60^(\circ)`

Adding both sides by 60, we get;

`148^(\circ)=\widehat{NQ}`

Thus, the measure of arc NQ is 148°