Question

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

Answer 1

Given:

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

`m\angle XYV=7x+21`

`m\angle UWY=91-7x`

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.

`\angle XYV \cong \angle UWY` [Corresponding angle]

`m\angle XYV=m\angle UWY`

`7x+21=91-7x`

We need to solve this equation for x.

`7x+7x=91-21`

`14x=70`

`x=(70)/(14)`

`x=5`

Now,

`m\angle XYV=7x+21`

`m\angle XYV=7(5)+21`

`m\angle XYV=35+21`

`m\angle XYV=56`

Therefore, the measure of angle XYV is 56 degrees.