Answer:
x = 24°
Step-by-step explanation:
If two parallel lines are being intersected by the same line, the opposite inside angles are congruent. This means that ∠EFH should be equal to ∠JHF. However, we cannot set these angles equal because we do not know the value of ∠JHG.
Line IG is intersected by line HJ. This means the value of ∠JHG is 24° (180° - 156° = 24°). Know that we know this value, we can set up an equation to find "x".
∠EFH = 2x
∠JHG = 24°
∠GHF = x
∠EFH = ∠JHF <----- Opposite interior angles are equal
∠EFH = ∠JHG + ∠GHF <----- Break ∠JHF into 2 angles
2x = 24 + x <----- Insert values
x = 24 <----- Subtract x from both sides
