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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

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Exercise 9 Page 764

The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs.

71.5

Practice makes perfect

Consider the given diagram.

We want to find m∠ 4. We know that if two secants or chords intersect inside the circle, then the measure of an angle formed is half the sum of the arcs intercepted by the angle and its vertical angle. m∠ 4 = 1/2(mST+ mRU) Let's substitute the known values and simplify.

m∠ 4 = 1/2(mST+mRU)

mST= 51, mRU= 92

m∠ 4 = 1/2(51+92)

Add terms

m∠ 4 = 1/2(143)

MoveRightFacToNum

a/c* b = a* b/c

m∠ 4 = 143/2

Calculate quotient

m∠ 4 = 71.5

Subchapter links

Exercises p.763-767