Question

In the diagram below of triangle B, C, DBCD, EE is the midpoint of start overline, B, D, end overline
BD
and FF is the midpoint of start overline, C, D, end overline
CD
. If mangle, D, C, B, equals, 135, minus, 9, x∠DCB=135−9x, and mangle, D, F, E, equals, 6, x, plus, 15∠DFE=6x+15, what is the measure of angle, D, F, E∠DFE?

Answer 1

E and F are midpoints of BD and CD, so EF is parallel to BC. Thus ∠DFE (between FD and FE) equals ∠DCB. Set them equal:

135 − 9x = 6x + 15
120 = 15x
x = 8

Then ∠DFE = 6x + 15 = 6(8) + 15 = 63°.

Answer: 63°.