SOLUTION: The difference between the measures of two consecutive angles of a paralellogram is 72. Find the measures of all the angles

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Question 1013939: The difference between the measures of two consecutive angles of a paralellogram is 72. Find the measures of all the angles
Answer by crabbyoldgamer(13) About Me  (Show Source):
You can put this solution on YOUR website!
In a parallelogram, consecutive angles are supplementary. They add to 180.


Let's call these consecutive angles x and y. Let x be the larger angle. We know two relationships between them:


x + y = 180 and x-y = 72


x-y = 72 ---> x = 72 + y: substitute this x value into the first equation.


72+y + y = 180


2y = 108


y = 54


x = 72 + y = 72 + 54 = 126


In a parallelogram opposite angles are congruent. So there are two angles that are 54 degrees, y and the angle opposite it, and there are two angles that are 126 degrees, x and the angle opposite it.