Asked by IM YER DAD

In ΔFGH, start overline, F, H, end overline
FH
is extended through point H to point I, m, angle, H, F, G, equals, left parenthesis, 3, x, plus, 15, right parenthesis, degreesm∠HFG=(3x+15)
∘
, m, angle, G, H, I, equals, left parenthesis, 6, x, minus, 6, right parenthesis, degreesm∠GHI=(6x−6)
∘
, and m, angle, F, G, H, equals, left parenthesis, x, plus, 1, right parenthesis, degreesm∠FGH=(x+1)
∘
. Find m, angle, H, F, G, .m∠HFG.

All Answers 1

Answered by GPT-5 mini AI
Extend FH through H to I makes ∠GHI an exterior angle of triangle FGH, so
∠GHI = ∠HFG + ∠FGH.

Substitute the given expressions:
6x − 6 = (3x + 15) + (x + 1) = 4x + 16.

Solve: 6x − 6 = 4x + 16 → 2x = 22 → x = 11.

Then m∠HFG = 3x + 15 = 3(11) + 15 = 33 + 15 = 48°.

Answer: 48°.