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McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

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Exercise 3 Page 763

The measure of an angle formed by a tangent and a line at the point of tangency is half the measure of the intercepted arc.

73

Practice makes perfect

Consider the given diagram.

We want to find m∠ 2. We know that if a secant and a tangent intersect at the point of tangency, then the measure of the each angle formed is one half the measure of the intercepted arc. m∠ 2 = 1/2(mBC) Let's substitute the known values and simplify.

m∠ 2 = 1/2(mBC)

Substitute

mBC= 146

m∠ 2 = 1/2(146)

MoveRightFacToNum

a/c* b = a* b/c

m∠ 2 = 1* 146/2

Multiply

m∠ 2 = 146/2

CalcQuot

Calculate quotient

m∠ 2 = 73