Final answer:
By setting up an equation based on the fact that line XY bisects angle WXZ and solving for x, we find that m angle WXZ is 62 degrees.
Step-by-step explanation:
If "line over XY" bisects ∠ WXZ, it means that ∠ WXY and ∠ YXZ are two equal angles and their measures add up to the measure of ∠ WXZ. Given that m ∠ WXY = 4x − 1 and m ∠ YXZ = 2x + 15, we can set up an equation since they are equal because of the bisection:
4x − 1 = 2x + 15
By solving the equation:
4x − 2x = 15 + 1
2x = 16
x = 8
Now, substitute x in either of the angle expressions to find the measure of that angle. Let's use m ∠ WXY:
m ∠ WXY = 4x − 1 = 4(8) − 1 = 32 − 1 = 31
Since ∠ WXY and ∠ YXZ are equal and we want the measure of the entire angle ∠ WXZ, we simply double the measure of one of the bisected angles:
m ∠ WXZ = 2 * m ∠ WXY = 2 * 31 = 62
So the measure of ∠ WXZ is 62 degrees.