The measure of the ∠1 is 35 degrees.
<h3>How to determine the angle </h3>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 =
∠ 1 =
∠ 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.
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