1. Define the variables:

* Let 'x' be the angle.

* Its supplementary angle is (180 - x).

2. Set up the equation:

The problem states that the angle is "quarter times greater than its supplementary angle," which translates to:

x = (1/4)(180 - x) + (1/4)(180 - x)

3. Solve for x:

* Simplify the equation: x = (1/2)(180 - x)

* Distribute: x = 90 - (1/2)x

* Add (1/2)x to both sides: (3/2)x = 90

* Multiply both sides by (2/3): x = 60

Therefore, the angle is 60 degrees.