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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Recall (or look up) that a sum of all the angles of a quadrilateral is ALWAYS 360 degrees.


So algebraically, this means that:


Start with the given equation.


Remove the parenthesis.


Combine like terms on the left side.


Divide both sides by to isolate .


Reduce.


Since , we can find the angles to be:


Angle #1:

Angle #2:

Angle #3:

Angle #4:


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


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