Angles in Quadrilateral

[nycmath]

In a quadrilateral two angles are equal. The third angle is equal to the sum of the two equal angles. The fourth angle is 60° less than twice the sum of the other three angles. Find the measures of the angles in the quadrilateral.

[Eigenvalue]

Let x be the measure of one of the equal angles

x+x+2x+2(4x)-60=360
4x+8x=420
12x=420
x=35

The angle measures of the quadrilateral are 35,35,70, and 220