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Question 1037714: If c=14x° & A=(3x+10)° what is the value of x in the isosceles trapezoid?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! An isosceles trapezoid looks like this:
 , with two congruent  angles and two congruent  angles.
The angles are supplementary to the angles.
The vertices in a trapezoid (or any polygon) are named going around in order (clockwise or counterclockwise).
No matter how the vertices in your isosceles trapezoid are named,
 and  angles are opposite vertices/angles.
The opposite angles in an isosceles trapezoid
(one acute and one obtuse) are supplementary,
meaning that their measures add up to  , so
 , meaning that  .
Now, all you have to do is solve that equation:
If we are curious, we can figure out the measures of the angles as
 and
 .
So, the isosceles trapezoid in the problem looks like this:
NOTE:
A rectangle is considered a special case of a trapezoid,
and it can be considered an isosceles trapezoid.
In that case, all four angles would measure  ,
with no acute or obtuse angle,
but opposite angles would still be supplementary.
That is not the case with the problem above,
but the reasoning above would have worked just the same,
even if we had figured out that both angles were right angles.
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