body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

Continue to next subchapter

Exercise 21 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.

185

Practice makes perfect

Consider the given diagram.

We want to find m XY. 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∠ W = 1/2(mXY-mZX) Let's substitute the known values in the expression and solve it for m XY.

m∠ W = 1/2(mXY - mZX)

m∠ W= 41, mZX= 103

41 = 1/2(mXY - 103)

LHS * 2=RHS* 2

82 = mXY - 103

LHS+103=RHS+103

185 = mXY

Rearrange equation

mXY = 185

Subchapter links

Exercises p.763-767