Find the sharp corners of a right triangle if one is 60 degrees larger than the other.

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

2. Determine the degree measure of the larger angle:

(x + 60˚).

3. Let’s compose and solve the equation:

(x + 60˚) + x + 90˚ = 180˚;

x + 60˚ + x + 90˚ = 180˚;

2x + 150˚ = 180˚;

2x = 180˚ – 150˚;

2x = 30˚;

x = 30˚: 2;

x = 15˚.

4. The degree measure of the smaller angle is x = 15˚.

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

x + 60˚ = 15˚ + 60˚ = 75˚.

Answer: The acute angles of a right-angled triangle are 15˚ and 75˚.