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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 23 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.

22

Practice makes perfect

Consider the given diagram.

We want to find m SU. 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∠ R = 1/2(mVT-mSU) Let's substitute the known values in the expression and solve it for m SU.

m∠ R = 1/2(mVT - mSU)

m∠ R= 23, mVT= 68

23 = 1/2(68 - mSU)

LHS * 2=RHS* 2

46 = 68 - mSU

LHS+mSU=RHS+mSU

mSU + 46 = 68

LHS-46=RHS-46

mSU = 22

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Exercises p.763-767