Find the measure (in degrees) of each angle. (Enter your answers from smallest to largest.)

Question

If the measures of the angles of a quadrilateral are in the ratio of 4 : 5 : 6 : 9, find the measure (in degrees) of each angle. (Enter your answers from smallest to largest.)

Answer 1

The formula for the sum of the measures of all interior angles of a 2-dimensional geometric figure are (n-2)*180, where n is the number of sides. So a quadrilateral has n=4, thus (4-2)*180=2*180=360 as the sum of all interior angle measures. If the ratio is 4:5:6:9, then we can add these 4+5+6+9=24. Then 360/24=15, so one angle is 4*15=60, one is 5*15=75, one is 6*15=90, and the last is 9*15=135.

Checking our work, we see that 60+75+90+135=360, as we expect.