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McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

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Exercise 5 Page 763

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.

248

Practice makes perfect

Consider the given diagram.

We want to find m QTS. We know that if two lines intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arc. 71^(∘) = 1/2(mQTS - 106^(∘) ) Let's solve it for mQTS.

71 = 1/2(mQTS - 106 )

MultEqn

LHS * 2=RHS* 2

142 = mQTS - 106

AddEqn

LHS+106=RHS+106

248 = mQTS

RearrangeEqn

Rearrange equation

mQTS = 248