In this diagram, EFGH is a parallelogram. Find the value of .
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Note that since ∠ S T H = 9 0 ∘ , ∠ E T F = ∠ K T H = 9 0 − ( 7 x − 1 0 ) = 1 0 0 − 7 x . Also note, using the fact that adjacent angles in a parallelogram are supplementary, that ∠ E = 1 3 9 ∘ .
Writing an equation for the sum of the angles in triangle ETF, we have:
( 1 0 0 − 7 x ) + 1 3 9 + ( x − 5 ) = 1 8 0
2 3 4 − 6 x = 1 8 0
− 6 x = − 5 4
x = 9