Answer to Question #306099 in Math for nick

Question #306099

In a quadrilateral, two angles are equal. The third angle is the sum of the two



equal angles. The fourth angle is 60º less than twice the sum of the other



angles. Find the measure of the largest angle. Make a sketch.




1
Expert's answer
2022-03-07T10:56:02-0500

The sum of the interior angles of a quadrilateral is 360°.


"\\alpha+\\beta+\\gamma+\\theta=360\\degree"

Given

"\\alpha=\\beta, \\gamma=\\alpha+\\beta"

"\\theta=2(\\alpha+\\beta+\\gamma)-60\\degree"

"\\alpha+\\beta+\\gamma=360\\degree-\\theta"

Substitute


"\\theta=2(360\\degree-\\theta)-60\\degree"

"3\\theta=660\\degree"

"\\theta=220\\degree"

"\\alpha+\\beta+\\gamma=360\\degree-220\\degree=140\\degree"

"\\alpha+\\alpha+2\\alpha=140\\degree"

"\\alpha=35\\degree=\\beta, \\gamma=2(35\\degree)=70\\degree"

The angles are

"35\\degree, 35\\degree, 70\\degree, 220\\degree"




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