SOLUTION: A quadrilateral's four angles measure x + 5, x + 10, x - 10, and 2x - 5. Find the measure of the largest angle.

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Question 198287: A quadrilateral's four angles measure x + 5, x + 10, x - 10, and 2x - 5. Find the measure of the largest angle.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Recall (or look up) that a sum of all the angles of a quadrilateral is ALWAYS 360 degrees.


So algebraically, this means that: %28x%2B5%29%2B%28x%2B10%29%2B%28x-10%29%2B%282x-5%29=360


%28x%2B5%29%2B%28x%2B10%29%2B%28x-10%29%2B%282x-5%29=360 Start with the given equation.


x%2B5%2Bx%2B10%2Bx-10%2B2x-5=360 Remove the parenthesis.


5x=360 Combine like terms on the left side.


x=%28360%29%2F%285%29 Divide both sides by 5 to isolate x.


x=72 Reduce.


Since x=72, we can find the angles to be:


Angle #1: x%2B5=72%2B5=77

Angle #2: x%2B10=72%2B10=82

Angle #3: x-10=72-10=62

Angle #4: 2x-5=2%2872%29-5=144-5=139


So we have the angles 77, 82, 62, and 139.


We can clearly see that the fourth angle of 139 degrees is the largest.