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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Inscribed Angles

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Exercise 13 Page 745

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

70

Practice makes perfect

An angle whose vertex is on a circle and whose sides are chords of the circle is an inscribed angle. Therefore, ∠ P is an inscribed angle. The measure of the intercepted arc of this angle is NQ.

Since the measure of a full turn around a circle is 360^(∘), we can use the Arc Addition Postulate to find mNQ.

120+100+ mNQ=360

Add terms

220+mNQ=360

LHS-220=RHS-220

mNQ= 140

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This means that m∠ P is half of m NQ.

m∠ P=m NQ/2

m NQ= 140

m∠ P=140/2

Calculate quotient

m∠ P=70

We found that m∠ P=70^(∘).

Subchapter links

Exercises p.745-748