Question

In circle K shown, the measure of NPL is twice the measure of NL . Which of the following is the measure

Answer 1

Please consider the complete question.

Let x represent measure of arc NL.

We have been given that measure of arc NPL is twice the measure of arc NL. So measure of arc NPL would be $2x$.

We know that measure of all arcs in a circle is equal to 360 degrees, so we can set an equation as:

$\widehat{NL}+\widehat{NPL}=360^{\circ}$

Upon substituting measure of both arcs, we will get:

$x+2x=360^{\circ}$

$3x=360^{\circ}$

$\frac{3x}{3}=\frac{360^{\circ}}{3}$

$x=120^{\circ}$

The measure of arc NPL would be $2x\Rightarrow 2(120^{\circ})=240^{\circ}$.

We can see that angle NML is inscribed angle of arc NPL. We know that measure of an inscribed angle is half the measure of intercepted arc.

$m\angle NML=\frac{1}{2}m\widehat{NPL}$

$m\angle NML=\frac{1}{2}\cdot 240^{\circ}$

$m\angle NML=120^{\circ}$

Therefore, the measure of angle NML is 120 degrees and 3rd option is the correct choice.