Question

In ΔFGH, start overline, F, H, end overline
FH
is extended through point H to point I, m, angle, F, G, H, equals, left parenthesis, 3, x, plus, 3, right parenthesis, degreesm∠FGH=(3x+3)
∘
, m, angle, H, F, G, equals, left parenthesis, 3, x, plus, 18, right parenthesis, degreesm∠HFG=(3x+18)
∘
, and m, angle, G, H, I, equals, left parenthesis, 9, x, minus, 6, right parenthesis, degreesm∠GHI=(9x−6)
∘
. Find m, angle, H, F, G, .m∠HFG.

Answer 1

Since HI is the extension of FH, ∠GHI is an exterior angle at H, so
∠GHI = ∠FGH + ∠HFG.

Substitute the given expressions:
9x − 6 = (3x + 3) + (3x + 18) = 6x + 21.

Solve:
9x − 6 = 6x + 21
3x = 27
x = 9.

Then m∠HFG = 3x + 18 = 3(9) + 18 = 27 + 18 = 45°.

Answer: 45°.