Exercise 19 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.

Practice makes perfect

Consider the given diagram.

We want to find m∠ W. 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(mXZY-mXY) Note that arcs XZY and XY form together a full turn around the origin. Using the Arc Addition Postulate, we can find the value of mXZY. mXZY = 360^(∘) - mXY Let's substitute the value of mXY and simplify.

mXZY = 360^(∘) - mXY

Substitute

mXY= 106

mXZY = 360^(∘) - 106

SubTerm

Subtract term

mXZY = 254

Now, we can use the value of mXZY that we have just discovered in the expression for m∠ W and simplify.

m∠ W = 1/2(mXZY - mXY)

SubstituteII

mXZY= 254, mXY= 106

m∠ W = 1/2(254- 106)