Question

In the diagram below of triangle D, E, FDEF, GG is the midpoint of start overline, D, F, end overline
DF
and HH is the midpoint of start overline, E, F, end overline
EF
. If mangle, F, D, E, equals, minus, 4, x, plus, 97∠FDE=−4x+97, and mangle, F, G, H, equals, 37, plus, 8, x∠FGH=37+8x, what is the measure of angle, F, D, E∠FDE?

Answer 1

G and H are midpoints of DF and EF, so GH is the midsegment of triangle DEF and is parallel to DE. Therefore ∠FGH and ∠FDE are corresponding (equal) angles.

Set them equal:
-4x + 97 = 37 + 8x
97 − 37 = 12x
60 = 12x
x = 5

Then ∠FDE = −4(5) + 97 = −20 + 97 = 77°.

Answer: 77°.