In the diagram below of triangle UVW, X is a midpoint of UV and Y is a midpoint of VW. If mZXYV = 7x + 21, and mZUWY = 91 – 7x,
what is the measure of ZXY?
V
X
Y
U
W

Given:

In triangle UVW, X is the midpoint of UV and Y is the midpoint of VW.

To find:

The measure of angle XYV.

Solution:

Since X is the midpoint of UV and Y is the midpoint of VW, therefore XY is the mid-segment of the triangle UVW and parallel to the base of the triangle, i.e., UW.

If a transversal line intersect two parallel lines, then the corresponding angles are congruent and their measures are equal.

        [Corresponding angle]

We need to solve this equation for x.

Now,

Therefore, the measure of angle XYV is 56 degrees.