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

Question 1058852: 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 Theo(13342) (Show Source): You can put this solution on YOUR website!
the sum of the 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 + y = 180.
the ratio of one of these angles to the other is 4/5.
this means that x/y = 4/5
solve for x to get x = 4/5 * y.
x + y = 180 becomes 4/5 * y + y = 180 which becomes 9/5 * y = 180.
solve for y to get y = 180 * 5 / 9 which is equal to 100.
this makes 4/5 * y = 80.
the sum of the consecutive angles is equal to 100 + 80 which is equal to 180.
this confirms the solution is correct.
one of the angles of the parallelogram is 100 degrees and the other angle is 80 degrees.
opposite angles are equal so you get sum of the angles of the parallelogram is equal to 2 * 100 + 2 * 80 which is equal to 360.
the sum of the angles of an quadrilateral have to be equal to 360, so the solution is confirmed to be correct again.
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