Half the measure of the angle is 25 more than one-third the measure of its supplement.
To find the solution, let's use the given information step by step.
Let's assume the angle is represented by "x". The supplement of x would be 180 degrees minus x. We are given that half the measure of the angle is 25 more than one-third of its supplement.
So, we can write this as:
(1/2)x = (1/3)(180 - x) + 25
To solve this equation, we'll simplify both sides step by step.
Multiply the right side of the equation by 3 to get rid of the fraction:
(1/2)x = (3/3)(180 - x) + 25
Simplify the equation further:
(1/2)x = 540/3 - (1/3)x + 25
Combine the terms on the right side:
(1/2)x = 180 - (1/3)x + 25
Now, let's adjust the equation to eliminate the fractions by multiplying through by the common denominator, which is 6:
6 * (1/2)x = 6 * (180 - (1/3)x + 25)
Simplify both sides:
3x = 6 * 180 - 2x + 6 * 25
Further simplification:
3x = 1080 - 2x + 150
Combine like terms:
3x + 2x = 1080 + 150
5x = 1230
Divide both sides by 5 to solve for x:
x = 1230 / 5
x = 246
Therefore, the measure of the angle is 246 degrees.