The supplement of an angle is one fifth of itself. Determine the larger angle.

Sure, let's solve this step by step:

1. Let's denote the angle as x. According to the problem, the supplement of the angle is one fifth of the angle itself. We know that supplementary angles add up to 180 degrees. Therefore, we can write the equation as x + 1/5x = 180.

2. To simplify the equation, we can multiply every term by 5 to get rid of the fraction: 5x + x = 900.

3. Combining like terms gives us 6x = 900.

4. Finally, solving for x by dividing both sides of the equation by 6 gives us x = 150.

So, the larger angle is 150 degrees.