The image shown has two triangles sharing a vertex: There are two triangles labeled UVW and WXZ with a common vertex W.

In triangle UVW:
- Angle VUW is labeled as y.
- Angle WVU is labeled as 50 degrees.

In triangle WXZ:
- Angle WXZ is labeled as 50 degrees.

What is the measure of ∠WZX, and why?

A. y/2, because triangle UVW is congruent to triangle WXZ.
B. y, because triangle UVW is similar to triangle ZXW.
C. y + 50 degrees, because triangle UVW is similar to triangle ZXW.
D. 130 degrees − y, because triangle UVW is congruent to triangle WXZ.

In the given problem, we have two triangles, UVW and WXZ, sharing a common vertex W. We're told that in triangle UVW, angle WVU is 50 degrees and angle VUW is labeled as y. In triangle WXZ, angle WXZ is 50 degrees. To find the measure of ∠WZX, we can use the fact that Triangle UVW is congruent to Triangle WXZ.

Congruent triangles have the same corresponding angles. In Triangle UVW, angle WVU is 50 degrees, so in Triangle WXZ, the corresponding angle would also be 50 degrees. Now, we can find the measure of ∠WZX by subtracting the sum of the angles in Triangle WXZ from 180 degrees (since the total angle sum in a triangle is 180 degrees):

∠WZX = 180 degrees - (50 degrees + 50 degrees)
∠WZX = 180 degrees - 100 degrees
∠WZX = 80 degrees

Now, we know that ∠WZX is 80 degrees. To relate it to the angle y, we can express it as 130 degrees minus y:

∠WZX = 130 degrees - y

So, the measure of ∠WZX is 130 degrees minus y, because Triangle UVW is congruent to Triangle WXZ.

Learn more about triangles angle

brainly.com/question/31911439

#SPJ11