https://file.aiquickdraw.com/mathbot/file/1726742608223t0pn0o98.jpg

Let's analyze the problem step by step.

The problem states:
- \( \overrightarrow{WY} \) bisects \( \angle XWZ \).
- \( m \angle YWZ = 49^\circ \).

We need to find:
1. \( m \angle XWY \)
2. \( m \angle XWZ \).

### Step 1: Use the fact that \( WY \) bisects \( \angle XWZ \)
Since \( WY \) bisects \( \angle XWZ \), it divides \( \angle XWZ \) into two equal parts. This means:
\[
m \angle XWY = m \angle YWZ = 49^\circ
\]

So, \( m \angle XWY = 49^\circ \).

### Step 2: Calculate \( m \angle XWZ \)
Since \( WY \) bisects \( \angle XWZ \) and each part is \( 49^\circ \), the total angle \( XWZ \) is twice \( 49^\circ \):
\[
m \angle XWZ = 49^\circ + 49^\circ = 98^\circ
\]

### Final answers:
- \( m \angle XWY = 49^\circ \)
- \( m \angle XWZ = 98^\circ \)

Would you like a further explanation or have any other questions?

Here are 5 related questions:
1. What does it mean for a line to bisect an angle?
2. How do you determine the total angle from two equal bisected angles?
3. What is the sum of angles in a triangle?
4. Can you explain what complementary and supplementary angles are?
5. How would you solve this problem if only one of the angles was given?

**Tip**: When dealing with bisected angles, always remember that each half is equal, and you can double one of them to find the full angle.

In the diagram, WY bisects ∠XWZ, and m∠YWZ = 49°. Find m∠XWY and m∠XWZ.

Learn how to solve a geometry problem involving an angle bisector where WY bisects ∠XWZ, and m∠YWZ is given as 49°. Follow step-by-step instructions to find m∠XWY and m∠XWZ using the Angle Bisector Theorem. Suitable for students in Grades 7-9.

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