Answer: 72
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Step-by-step explanation:
The two angles shown are vertical angles. Such angles are opposite one another in an X configuration like this. They don't have to be vertically aligned.
Vertical angles are always congruent.
angle DHG = angle EHF
6(x-2) = 3x+30
6x-12 = 3x+30
6x-3x = 30+12
3x = 42
x = 42/3
x = 14
Then use that x value to find each angle.
- angle DHG = 6(x-2) = 6(14-2) = 6(12) = 72
- angle EHF = 3x+30 = 3(14)+30 = 42+30 = 72
The fact we get the same result (72) each time confirms we have the correct x value, and it confirms the overall answer.