Question

5 times the measure of the complement of an angle is to equal to 2/3 the measure of the original angle's supplement. what is the measure of the angle?

Answer 1

Let x be the measure of the angle. The mathematical equation of the problem is
5(90-x) =
`(2)/(3)`(180-x)

`(450 - 5x) = (2)/(3)(180 - x) \\ 3(450 -5x) = 360 - 2x \\ 1350 -15x =360 -2x \\ 15x - 2x = 1350 - 360 \\ 13x = 990 \\ x=76.15 The measure of the angle is 76.15`°