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˚.
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