Respuesta :

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 [tex]2x[/tex].

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

[tex]\widehat{NL}+\widehat{NPL}=360^{\circ}[/tex]

Upon substituting measure of both arcs, we will get:

[tex]x+2x=360^{\circ}[/tex]

[tex]3x=360^{\circ}[/tex]

[tex]\frac{3x}{3}=\frac{360^{\circ}}{3}[/tex]

[tex]x=120^{\circ}[/tex]

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

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.

[tex]m\angle NML=\frac{1}{2}m\widehat{NPL}[/tex]

[tex]m\angle NML=\frac{1}{2}\cdot 240^{\circ}[/tex]

[tex]m\angle NML=120^{\circ}[/tex]

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

Ver imagen ApusApus
akposevictor

Based on the inscribed angle theorem, the measure of ∠NML is: 120°.

What is the Inscribed Angle Theorem?

If an angle is inscribed in a circle, its measure would be half its intercepted arc.

First, find m(NPL):

Let the measure of arc NL = x

The measure of arc NPL = 2x

Full circle = 360°, therefore:

2x + x = 360

3x = 360

x = 360/3

x = 120

Measure of arc NPL = 2x = 2(120) = 240°.

Based on the inscribed angle theorem, we will have:

m∠NML = 1/2(Measure of arc NPL)

m∠NML = 1/2(240)

m∠NML = 120°

Therefore, based on the inscribed angle theorem, the measure of ∠NML is: 120°.

Learn more about the inscribed angle theorem on:

https://brainly.com/question/3538263