SOLUTION: in a quadrilateral two angles are equal. the third angle has a measure that is equal to the sum of the equal angles. the fourth angle is 75 degrees less than twice the sum of the o

Algebra ->  Angles -> SOLUTION: in a quadrilateral two angles are equal. the third angle has a measure that is equal to the sum of the equal angles. the fourth angle is 75 degrees less than twice the sum of the o      Log On


   

Question 904539: in a quadrilateral two angles are equal. the third angle has a measure that is equal to the sum of the equal angles. the fourth angle is 75 degrees less than twice the sum of the other three angles. what are the measures of the angles?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let one of the angles be equal to x.
the other angle that's equal to it is also equal to x.
the third angle is equal to the sum of the two equal angles so the third angle is equal to 2x.
the fourth angle is equal to 75.
the sum of the angles in a quadrilateral is 360 degrees.
you get x + x + 2x + 75 = 360
combine like terms to get 4x + 75 = 360
subtract 75 from both sides of the equation to get 4x = 285
divide both sides of the equation by 4 to get x = 71.25
the angles are:
71.25
71.25
142.5
75
add them up and you get 360 degrees.