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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 18 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.

81

Practice makes perfect

Consider the given diagram.

We want to find m∠ A. 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∠ A = 1/2(mBDC-mCB) Note that arcs BDC and CB form together a full turn around the origin. Using the Arc Addition Postulate, we can write an expression for mBDC . mBDC = 360^(∘) - mCB Let's substitute the value of mCB and simplify.

mBDC = 360 - mCB
Substitute

mCB= 99

mBDC = 360 - 99
SubTerm

Subtract term

mBDC = 261

Now, we can substitute mBDC and mCB in the expression for m∠ A and simplify.

m∠ A = 1/2(mBDC - mCB)
SubstituteII

mBDC= 261, mCB= 99

m∠ A = 1/2( 261 - 99)
SubTerm

Subtract term

m∠ A = 1/2(162)
MoveRightFacToNum

a/c* b = a* b/c

m∠ A = 1 * 162/2
Multiply

Multiply

m∠ A = 162/2
CalcQuot

Calculate quotient

m∠ A = 81
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