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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 20 Page 764

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

205

Practice makes perfect

Consider the given diagram.

We want to find m JM. We know that if two lines intersect outside a circle, the measure of the angle formed by the intersection of the lines is half the difference of the measures of the intercepted arcs. m∠ K = 1/2(mJM-mLJ) Let's substitute the known values in the expression and solve it for m JM.

m∠ K = 1/2(mJM - mLJ)

mLJ= 111, m∠ K= 47

47 = 1/2(mJM - 111)

LHS * 2=RHS* 2

94 = mJM - 111

LHS+111=RHS+111

205 = mJM

Rearrange equation

mJM = 205

Subchapter links

Exercises p.763-767