We know that the two angles are congruent (equal in measure), so we take the written out descriptions of the angles and convert them to equations that we set equal to each other.
"Three more than twice a number" = 2x + 3
"54.5 less than three times the number" = 3x - 54.5
2x + 3 = 3x - 54.5
Add 54.5 to both sides
2x + 57.5 = 3x
Subtract 2x from both sides
57.5 = x
Now we plug in 57.5 in the original equations to get the measure of each angle.
2(57.5) + 3 = 118 degrees
3(57.5) - 54.5 = 118 degrees
As we already knew, the angles are congruent.
P.S.: Nowhere in the prompt does it say anything about a triangle, just that we have a pair of congruent angles. Be sure to read each prompt carefully.