Question

In the diagram of circle A, what is m?

75°
90°
120°
135°

Answer 1

Answer:

90

Step-by-step explanation:

Alright first step what is the degree measure of LN.

A full rotation is 360 degrees so LN=360-270=90.

So angle M is half the difference of the intercepted arcs:

$\frac{1}{2}(270-90)=\frac{1}{2}(180)=90$

Answer 2

The measure of the vertex angle from the given geometry figure is 90 degrees

Circle geometry

The given circle is made up of arc and angles. In order to determine the value of <M, we will use the theorem

"The half of the difference between the arc is equal to the angle at the vertex

1/2(270 - (360 - 270)) = <M
<M = 1/2 (270 -90)

<M = 1/2(180)

<M = 90degrees

Hence the measure of the vertex angle from the given geometry figure is 90 degrees

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