SOLUTION: The ratio of the angle measures of a quadrilateral is 4:9:5:6. What is the measure of the smallest angle? Thanks for your help.

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Question 311309: The ratio of the angle measures of a quadrilateral is 4:9:5:6. What is the measure of the smallest angle?
Thanks for your help.

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Every quadrilateral in a plane contains a total of 360 degrees.
If the ratio of the interior angles is 4:9:5:6, we can set them equal to
4x, 9x, 5x and 6x, and then set their sum equal to 360 degrees.
Thus 4x + 9x + 5x + 6x = 360
24x = 360
x = 15
and the angles are then
60, 135, 75, and 90 degrees, respectively.