The measure of angles are 137.5 degrees and 42.5 degrees
Solution:
Given that two angles are supplementary
Let "a" be the one of supplementary angle
Let "b" be the other supplementary angle
Given that measure of one angle is 10 degree more than three times the other
measure of one angle = 10 + three times the other angle
a = 10 + 3b ---- eqn 1
We know that,
Two Angles are Supplementary when they add up to 180 degrees.
a + b = 180 ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "b"
Substitute eqn 1 in eqn 2
10 + 3b + b = 180
10 + 4b = 180
4b = 170
b = 42.5
From eqn 1,
a = 10 + 3(42.5)
a = 10 + 127.5 = 137.5
a = 137.5
Thus the measure of angles are 137.5 degrees and 42.5 degrees