Question

In the diagram below of triangle C, D, ECDE, FF is the midpoint of start overline, C, E, end overline
CE
and GG is the midpoint of start overline, D, E, end overline
DE
. If mangle, E, D, C, equals, 99, minus, 9, x∠EDC=99−9x, and mangle, E, G, F, equals, 8, x, minus, 3∠EGF=8x−3, what is the measure of angle, E, D, C∠EDC?

Answer 1

FG is a midsegment (F and G are midpoints of CE and DE), so FG ∥ CD. Thus ∠EGF is congruent to ∠EDC. Set the expressions equal:

99 − 9x = 8x − 3
99 + 3 = 17x
102 = 17x
x = 6

Then ∠EDC = 99 − 9x = 99 − 54 = 45°.