Let Angle 1 = m, and let Angle 2 = n.
n measures 6 degrees less than twice m, so:
n=2m-6
Supplementary Angles add up to 180 deg, so:
m+n=180
m+2m-6=180
3m-6=180
3m=186
m=62 degrees
Therefore:
n=2m-6
n=2(62)-6
n=124-6
n=118 degrees
The two angles are 62 degrees, and 118 degrees.
