Final answer:
The measure of angle xyz is 64° since ray yw as the angle bisector results in two congruent angles, each of 32°.
Step-by-step explanation:
The student is asking about the measure of an angle when given the measure of its bisected angle. Since ray yw is the angle bisector of ∡xyz and m∡xyw = 32°, to find m∡xyz we simply need to understand that the angle bisector divides an angle into two congruent angles. Therefore, m∡xyz is twice the measure of m∡xyw, because the angle is bisected into two equal parts. So, m∡xyz = 2 × m∡xyw = 2 × 32° = 64°. This is a concept from geometry involving angle properties and bisectors.