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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 13 Page 764

The measure of an angle formed by a tangent and a line at the point of tangency is half the measure of the intercepted arc.

144

Practice makes perfect

Consider the given diagram.

We want to find mPM. We know that if a secant and a tangent intersect at the point of tangency, then the measure of the each angle formed is one half the measure of the intercepted arc. m∠ M = 1/2(mPM) Let's substitute the known values and solve it for mPM.

m∠ M = 1/2(mPM)

m∠M= 72

72 = 1/2(mPM)

LHS * 2=RHS* 2

144 = mPM

Rearrange equation

mPM = 144

Subchapter links

Exercises p.763-767