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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 24 Page 793

The Inscribed Angle Theorem tells us that the measure of an inscribed angle is half the measure of its intercepted arc.

109

Practice makes perfect

In our exercise we want to find the measure of ∠ 1.

To do so, let's recall the Inscribed Angle Theorem.

Inscribed Angle Theorem
The measure of an inscribed angle is half that of its intercepted arc.

An angle whose vertex is on a circle and whose sides are chords of the circle is an inscribed angle. Therefore, in the given diagram ∠ 1 is an inscribed angle and the intercepted arc of this angle has a measure of 218^(∘). This means that m∠ 1 is half of 218^(∘). m∠ 1 =1/2* 218^(∘) ⇕ m∠ 1=109^(∘)

Subchapter links

1 Circles and Circumference p.792

2 Measuring Angles and Arcs p.792

3 Arcs and Chords p.793

4 Inscribed Angles p.793

5 Tangents p.794

6 Secants, Tangents, and Angle Measures p.794

7 Special Segments in a Circle p.795

8 Equations of Circles p.795

9 Areas of Circles and Sectors p.796