Chapter 9.5, Problem 1CE

To determine

To explain: $\angle 1\cong \angle 2$ for the given figure.

Explanation of Solution

Given information:

Given figure,

Calculation:

The corollary is;

In a circle, two inscribed angles with the same intercept arc are congruent.

Consider the theorem:

The measure of an inscribed angle is equal to half the measure of its intercepted arc.

Proof:

The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.

Therefore, the angles are congruent that is $\angle 1\cong \angle 2$ .