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In reference to the image attached: Is it possible to solve for x despite the fact that...

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disaza | (Level 1) Adjunct Educator

Posted July 25, 2013 at 6:12 PM via web

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In reference to the image attached:

Is it possible to solve for x despite the fact that I don't know almost anything about the location of point E? If so, how could this be done?

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted July 25, 2013 at 7:52 PM (Answer #1)

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There is not enough information to solve this problem.

However, you can determine a fomula to find x.

Because AB is parallel to CD and AD if parallel to BC, we know that ABCD form a parallelogram. 

In a parallelogram, opposite angles are congruent.

Therefore, 
`/_` ADC = `/_` ABC
Both angles are equal to x.

We also know ABE is a triangle and the sum of the angles of a triangle is 180 degrees.

Keep in mind that `/_` ABC + `/_` CBE = `/_` ABE
`/_` ABE = x + 20

Therefore,
`/_` EAB + `/_` ABE + `/_` AEB = 180
50 + x + 20 + `/_` AEB = 180
70 + x + `/_` AEB = 180
x + `/_` AEB = 110
x = 110 - `/_` AEB

If you are given the measure of `/_` AEB, you can use the formula above to find x.

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