The measure of the supplement angle is 54 degrees.
Explanation:
Let's denote the measure of the obtuse angle as x.
One-half of the obtuse angle is 9 more than its supplement,
The supplement of an angle is 180 degrees minus the angle itself. Therefore, the supplement of the obtuse angle is 180 - x.
The equation based on the given information:
(1/2)x = (180 - x) + 9
Solve for x:
(1/2)x = 189 - x
Multiply both sides of the equation by 2 to eliminate the fraction:
x = 2(189 - x)
x = 378 - 2x
Add 2x to both sides of the equation:
x+2x = 378 -2x+2x
3x = 378
Divide both sides of the equation by 3:
x = 378 / 3
x = 126
Therefore, the measure of the obtuse angle is 126 degrees.
To find the measure of the supplement, subtract the obtuse angle from 180:
Supplement = 180 - x = 180 - 126 = 54 degrees
Hence, the measure of the supplement is 54 degrees.