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