Question

In the diagram below of triangle S, T, USTU, VV is the midpoint of start overline, S, U, end overline
SU
and WW is the midpoint of start overline, T, U, end overline
TU
. If mangle, U, T, S, equals, 80, minus, 4, x∠UTS=80−4x, and mangle, U, W, V, equals, 4, x, plus, 56∠UWV=4x+56, what is the measure of angle, U, T, S∠UTS?

Answer 1

VW connects midpoints of SU and TU, so VW ∥ ST. Thus ∠UWV (angle between UW which lies on TU, and WV which is parallel to ST) equals ∠UTS. Set them equal:

4x + 56 = 80 − 4x
8x = 24
x = 3

Then ∠UTS = 80 − 4x = 80 − 12 = 68°.