The sides of two corners are mutually perpendicular. One of them is 54 degrees larger than the other. Find these corners.

1. Let’s denote the degree measure of the smaller angle through x.

2. Determine the degree measure of the larger angle:

(x + 54˚).

3. Since the sides of the two angles are mutually perpendicular, we compose and solve the equation:

(x + 54˚) + x = 90˚;

x + 54˚ + x = 90˚;

2x + 54˚ = 90˚;

2x = 90˚ – 54˚;

2x = 36˚;

x = 36˚: 2;

x = 18˚.

4. The degree measure of the smaller angle is x = 18˚.

5. What is the degree measure of the larger angle?

x + 54˚ = 18˚ + 54˚ = 72˚.

Answer: The degree of the smaller angle is 18˚, the degree of the larger angle is 72˚.