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.

$7x+7x=91-21$

$14x=70$

$x=\dfrac{70}{14}$

$x=5$

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.