The measures of both the angles are 163 degrees and 17 degrees
Solution:
Given that two angles are supplementary
Let one of the angle be "x"
Let the other angle be "y"
Two angles are supplementary when add up to 180 degrees
x + y = 180 ----- eqn 1
Given that One angle measures 10 more than 9 times the other
x = 10 + 9y ----- eqn 2
Substitute eqn 2 in eqn 1
10 + 9y + y = 180
10 + 10y = 180
10y = 180 - 10
10y = 170
y = 17
Substitute y = 17 in eqn 2
x = 10 + 9(17)
x = 10 + 153
x = 163
Thus the measures of both the angles are 163 degrees and 17 degrees