SOLUTION: Two consecutive angles of a parallelogram are in the ratio 4:5.How many degrees are there in each angle of the parallelogram?

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Question 1129631: Two consecutive angles of a parallelogram are in the ratio 4:5.How many degrees are there in each angle of the parallelogram?
Answer by MathLover1(20850) About Me  (Show Source):
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by definition, the sum of the angles for each quadrilateral is 360°
the sum of the two consecutive angles of a parallelogram have to be equal to 180 degrees
let x = one of the angles and let+y = the other angle.
x+%2B+y+=+180
the ratio of one of these angles to the other is 4%2F5
this means that x%2Fy+=+4%2F5
solve for x to get x+=+%284%2F5%29+y
then x+%2B+y+=+180 becomes

%284%2F5%29+y+%2B+y+=+180 ....solve for y
%284%2F5%29+y+%2B%285%2F5%29+y+=+180
%289%2F5%29+y+=+180
+y+=+180%2F%289%2F5%29
+y+=+%28180%2A5%29%2F9
+y+=+%28cross%28180%2920%2A5%29%2Fcross%289%29
+y+=+100
then, x+%2B+100+=+180=> x=80
the sum of two consecutive angles is equal to 100+%2B+80+=+180
this confirms the solution is correct.
check the ratio:
80%2F100=4%2F5
8%2F10=4%2F5
4%2F5=4%2F5=> proves that angles of a parallelogram are in the ratio 4%3A5