Big Ideas Math Integrated II
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Exercise 1 Page 633

By the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. Also, the measure of a central angle equals the measure of its intercepted arc.

m∠1=72.5^(∘), m∠2=145^(∘)

Consider the given diagram.

We will find the measures of ∠1 and ∠2 one at a time.

Finding ∠1

By the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. With this in mind, we can find the measure of the inscribed angle in the given diagram.

By the theorem, we can calculate the measure of ∠1.

m∠1=145/2=72.5^(∘)

Finding ∠2

Now, we will find the measure of ∠2 which is a central angle.

Since the measure of a central angle is equal to the measure of its intercepted arc, we can identify the measure of ∠2 as follows.

m∠2=145 ^(∘)