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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
6. Secants, Tangents, and Angle Measures
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Exercise 42 Page 767

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.

C

Practice makes perfect

Consider the given diagram.

We want to find the value of x. 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. x = 1/2(mRP-mNR) Note that PN, NR and RP form together a full turn around the origin. Using the Arc Addition Postulate, we can write an expression for mRP. mRP = 360^(∘) - mPN - mRN

mRP = 360 - mPN - mRN
SubstituteII

mPN= 108, mRN= 62

mRP = 360 - 108 - 62
SubTerms

Subtract terms

mRP = 190

Now, we can substitute the known values in the expression for x and simplify.

x = 1/2(mRP - mRN)
SubstituteII

mRP= 190, mRN= 62

x = 1/2(190- 62)
SubTerm

Subtract term

x = 1/2(128)
MoveRightFacToNum

a/c* b = a* b/c

x = 1 * 128/2
Multiply

Multiply

x = 128/2
CalcQuot

Calculate quotient

x = 64

Therefore, the correct answer is C.

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