Persnickety Parallelogram

Geometry Level 2

In this diagram, EFGH is a parallelogram. Find the value of x x .


The answer is 9.

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1 solution

M M
Nov 22, 2016

Note that since S T H = 9 0 \angle STH = 90^\circ , E T F = K T H = 90 ( 7 x 10 ) = 100 7 x \angle ETF = \angle KTH = 90 - (7x - 10) = 100 - 7x . Also note, using the fact that adjacent angles in a parallelogram are supplementary, that E = 13 9 \angle E = 139^\circ .

Writing an equation for the sum of the angles in triangle ETF, we have:

( 100 7 x ) + 139 + ( x 5 ) = 180 (100-7x) + 139 + (x - 5) = 180

234 6 x = 180 234 - 6x = 180

6 x = 54 -6x = -54

x = 9 x = 9

Your first statement is a little odd as written. You want to justify something with the angles adding to 90, but the bit that immediately follows uses vertical angles. You can either separate angles ETF and KTH being equal in a separate statement or change the order so the vertical angles are applied after the 90 degree angle.

Jason Dyer Staff - 4 years, 6 months ago

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