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Answer:
- x = 3
- ∠IEH = 61°
- ∠IHE = 35°
Step-by-step explanation:
There are a couple of useful facts about parallelograms that can be used here.
1) The diagonals bisect each other.
2) Opposite sides are parallel, so each diagonal can be considered a "transversal" with respect to parallel lines. That means all of the angle relationships involving parallel lines apply.
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The two marked sections of diagonal GIE are congruent, so you have ...
3x +1 = 10
3x = 9 . . . . subtract 1
x = 3 . . . . . divide by 3
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Angles IEH and IGF are "alternate interior" angles, so are congruent.
angle IEH = 61°
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Angles IHE and IFG are "alternate interior" angles, so are congruent.
angle IHE = 35°
