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McGraw Hill Integrated II, 2012 View details

4. Inscribed Angles

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Exercise 1 Page 745

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

30

Practice makes perfect

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, ∠ B is an inscribed angle. The intercepted arc of this angle has a measure of 60^(∘).

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This means that m ∠ B is half of 60^(∘).

m ∠ B=60/2

CalcQuot

Calculate quotient

m ∠ B=30

We found that m∠ B= 30.