Let's break down each of the problems based on the image.

Problem 29:

• You are given that $\overline{WZ}$ bisects $\angle XWY$ and that $\angle XWZ = 52^\circ$.
• Since $\overline{WZ}$ is an angle bisector, this means that $\angle ZWY = \angle XWZ$.
• Therefore, $\angle ZWY = 52^\circ$.
• The total $\angle XWY = \angle XWZ + \angle ZWY = 52^\circ + 52^\circ = 104^\circ$.

Problem 30:

• Here, you are given that $\overline{WZ}$ bisects $\angle XWY$ and that $\angle ZWY = 68^\circ$.
• Since $\overline{WZ}$ bisects $\angle XWY$, $\angle XWZ = \angle ZWY = 68^\circ$.
• The total $\angle XWY = \angle XWZ + \angle ZWY = 68^\circ + 68^\circ = 136^\circ$.

Problem 31:

• In this case, you are given $\angle XWY = 71^\circ$, and $\overline{WZ}$ bisects $\angle XWY$.
• Since $\overline{WZ}$ bisects $\angle XWY$, $\angle XWZ = \angle ZWY$.
• Therefore, $\angle XWZ = \angle ZWY = \frac{71^\circ}{2} = 35.5^\circ$.

Summary of Missing Angles:

1. Problem 29:

   • $\angle ZWY = 52^\circ$
   • $\angle XWY = 104^\circ$

2. Problem 30:

   • $\angle XWZ = 68^\circ$
   • $\angle XWY = 136^\circ$

3. Problem 31:

   • $\angle XWZ = 35.5^\circ$
   • $\angle ZWY = 35.5^\circ$

Would you like more details on any of these problems or have any questions?

Related Questions:

1. How do you calculate the total angle $\angle XWY$ if given one of the bisected angles?
2. What is the relationship between an angle bisector and the two angles it creates?
3. Can you apply the angle bisector concept in a triangle to find unknown angles?
4. What is the sum of interior angles in a triangle, and how does the angle bisector affect it?
5. How would you find the missing angle in a situation where the total angle and one bisected part are known?

Tip:

An angle bisector divides an angle into two equal smaller angles, and this property can be applied in different geometric situations, like in triangles or polygons.