Question

Circle C is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is 36 degrees, and the second arc formed is 106 degrees.

In the diagram of circle C, what is the measure of ∠1?
17°
35°
70°
71°

Answer 1

The measure of the ∠1 is 35 degrees.

How to determine the angle

it is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.

Also, the angle subtended by the arc at the center of the circle is the angle of the arc

From the diagram, we have

m ∠ of external angle = half of the difference of arc angles

The arc angles are

• 106°
• 36°

m ∠ of external angle = ∠ 1

Let's substitute the angles

∠1 = $\frac{106 - 36}{2}$

∠ 1 = $\frac{70}{2}$

∠ 1 = 35°

We can see that the external angle 1 measures 35 degrees.

Note that the complete image is added.

Thus, the measure of the ∠1 is 35 degrees.

Learn more about a circle here:

https://brainly.com/question/15673093

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