SOLUTION: In a quadrilateral, the sum of the measures of all the four angles is 360 degrees. Suppose a quadrilateral has two angles that are equal. Also a third angle is equal to the sum of

Question 973151: In a quadrilateral, the sum of the measures of all the four angles is 360 degrees. Suppose a quadrilateral has two angles that are equal. Also a third angle is equal to the sum of the two equal angles. The fourth is 60 degrees less than twice the sum of the other three angles. Find the measures of the angles in the quadrilateral.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Let the measures of the angles be x, x, y and z.

According to the description and assigned variables,
.
Forming that system is the first objective in the solution process. Solving the system for x, y, and z is the second objective of the solution and will reach the finish.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
In a quadrilateral, the sum of the measures of all the four angles is 360 degrees. Suppose a quadrilateral has two angles that are equal. Also a third angle is equal to the sum of the two equal angles. The fourth is 60 degrees less than twice the sum of the other three angles. Find the measures of the angles in the quadrilateral.

Let measure of each of the 2 equal angles, be A
Then sum of the 2 equal angles = 2A
Third angle: 2A
Fourth angle: 2(A + A + 2A) - 60, or 2(4A) - 60, or 8A - 60
This results in: A + A + 2A + 8A - 60 = 360
12A - 60 = 360
12A = 360 + 60
12A = 420
A, or measure of each equal angle = , or
Measure of 3rd angle: 2(35), or
Measure of 4th angle: 8(35) - 60, or 280 - 60, or
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