Answer: 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.
