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.