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

Because X and Y are midpoints, XY is parallel to UV (midsegment). So ∠WXY is congruent to ∠WUV. Set them equal:

8x + 18 = 43 + 3x
5x = 25
x = 5

Then ∠WXY = 43 + 3x = 43 + 15 = 58°

Answer: 58°.