Question

If midpoint of DE and H is a midpoint, and if m∠GHE = 10x + 16, and FH = 8x + 24, what is the measure of ∠GHE?

a) 10x + 16
b) 8x + 24
c) 5x + 20
d) 18x + 40

Answer 1

If the midpoint of DE and H is a midpoint, and FH = 8x + 24, we can find the measure of angle GHE.

Step-by-step explanation:

Given that the midpoint of DE and H is a midpoint, we can conclude that DH = HE.

Since FH = 8x + 24, and FH represents the whole line, then DH = EH = (8x + 24) / 2 = 4x + 12.

Now, since GH is half of DE, GH = DH / 2 = (4x + 12) / 2 = 2x + 6.

Finally, using the angle relationship in a triangle, we have m∠GHE = m∠GHF = 10x + 16.