SOLUTION

EXAMPLE 5 Double an angle measure

In the diagram at the right, YW bisects XYZ, and m XYW = 18. Find m XYZ.

o

By the Angle Addition Postulate, m XYZ = m XYW + m WYZ. Because YW bisects XYZ you know that XYW WYZ. ~

So, m XYW = m WYZ, and you can write

M XYZ = m XYW + m WYZ = 18° + 18° = 36°.

GUIDED PRACTICE for Example 5

7. Angle MNP is a straight angle, and NQ bisects MNP. Draw MNP And NQ . Use arcs to mark the congruent angles in your diagram, and give

the angle measures of these congruent angles.

SOLUTION

GUIDED PRACTICE for Example 5

The solution is = 90°m MNQ = m PNQ

m MNQ + m PNQ = 180°

m MNQ + m PNQ

m MNQ + m MNQ = 180°

m MNQ2 = 180°

m MNQ = 90°

Angle addition postulate

Straight angle

m MNQ = m PNQ

Add

Divided each side by 2