Question

In the diagram below of triangle U, V, WUVW, XX is the midpoint of start overline, U, W, end overline
UW
and YY is the midpoint of start overline, V, W, end overline
VW
. If mangle, W, U, V, equals, 8, x, plus, 18∠WUV=8x+18, and mangle, W, X, Y, equals, 43, plus, 3, x∠WXY=43+3x, what is the measure of angle, W, X, Y∠WXY?

Answer 1

To find the measure of angle WXY, we first need to use the fact that XX is the midpoint of UW and YY is the midpoint of VW. This means that triangle WXY is a midsegment of triangle UWV.

Since XX is the midpoint of UW, we know that angle WXU is congruent to angle WXX. Similarly, since YY is the midpoint of VW, angle WYV is congruent to angle VYY.

Therefore, we can set up an equation using the fact that the sum of the angles in a triangle is 180 degrees:

angle W + angle WXY + angle WUV = 180

Substitute the given values for angles WUV and W:

8x + 18 + 43 + 3x = 180
11x + 61 = 180
11x = 119
x = 10.82

Now we can find the measure of angle WXY:

angle WXY = 43 + 3(10.82)
angle WXY = 43 + 32.46
angle WXY = 75.46 degrees

Therefore, the measure of angle WXY is 75.46 degrees.