One angle is twice its supplement increased by 54 degrees. find the measures of the two supplementary angles.

The two angles are 24 degrees and 156 degrees

Explanation:

Let x and y be the two supplementary angles

"one angle is twice its supplement increased by 54 degrees"

means that

y = 2(x+54)

Whatever angle x is, we add on 54, then double it to get angle y.

x+y = 180 since they are supplementary angles

x+2(x+54) = 180 plug in y = 2(x+54)

x+2x+108 = 180

3x = 180-108

3x = 72

x = 72/3

x = 24

y = 2(x+54)

y = 2(24+54)

y = 156

as a check

x+y = 24+156 = 180

so x and y are confirmed to be supplementary angles.