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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 22 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.

30

Practice makes perfect

Consider the given diagram.

We want to find m∠ R. 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(mQS-mUT) Let's substitute the known values in the expression and solve it for m∠ R.

m∠ R = 1/2(mQS - mUT)

mQS= 103, mUT= 43

m∠ R = 1/2(103 - 43)

Subtract term

m∠ R = 1/2(60)

MoveRightFacToNum

a/c* b = a* b/c

m∠ R = 1 * 60/2

Multiply

m∠ R = 60/2

Calculate quotient

m∠ R = 30

Subchapter links

Exercises p.763-767