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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 13 Page 749

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

85^(∘)

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 angle A is an inscribed angle. To help us find m∠ A we have been told that the measure of the intercepted arc BC is 170^(∘).

A circle with an intercepted arc with the measure 170 degrees

Let's recall the Inscribed Angle Theorem.

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

To find the measure of the intercepted angle we need to divide the measure of the intercepted arc by 2. m∠ A=170/2=85^(∘)

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