The measure of the complement of an angle and supplement of an angle are in the ratio of 2:7. Find the measure of the angle.

Answer 1

Hi Michelle,

Equate (90-x)/(180-x) with 2/7 and solve for x:

Cross multiply and set equal:

7(90-x)=2(180-x)

630-7x=360-2x

270=5x

x=54 degrees

Answer 2

Let x be the angle, in degrees. Its complement is 90 - x and its supplement is 180 - x. These are in the ratio 2:7, so (90 - x)/(180 - x) = 2/7. Solve, to get x = 54 deg. Plugging to check gives 36/126 = (2)(18)/(7)(18) = 2/7.

T Dupuis