In the diagram of circle C, what is the measure of < 1?

Solution:

We have to find the measure of ∠1.

From the given figure,

Measure of one arc = 106°

Measure of another arc = 36°

We know that if two secants intersect outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

So, difference of the intercepted arcs = 106° - 36° = 70°

∠1 = (1/2)(70°)

∠1 = 35°

Therefore, the measure of ∠1 is 35°.

In the diagram of circle C, what is the measure of <1?

Summary:

In the diagram of circle C, the measure of <1 is 35°.