Question

In the diagram below of triangle F, G, HFGH, II is the midpoint of start overline, F, H, end overline
FH
and JJ is the midpoint of start overline, G, H, end overline
GH
. If mangle, H, G, F, equals, 8, x, plus, 36∠HGF=8x+36, and mangle, H, J, I, equals, 3, x, plus, 66∠HJI=3x+66, what is the measure of angle, H, G, F∠HGF?

Answer 1

IJ joins midpoints of FH and GH, so IJ is parallel to FG. Therefore ∠HJI is congruent to ∠HGF, so

8x + 36 = 3x + 66
5x = 30
x = 6.

Thus ∠HGF = 8(6) + 36 = 48 + 36 = 84°.