One of the acute angles of a right-angled triangle is 32 ° smaller than the other, find the smaller angle of the triangle.

It is known from the condition that one of the acute angles of a right-angled triangle is 32 ° less than the other. In order to find the smaller angle of the triangle, we will compose and solve a linear equation.

Let us denote by the variable x the degree measure of one of the acute angles, then the second acute angle can be written as (x – 32).

The angles of a triangle add up to 180 °. Based on this, we will compose and solve the equation.

x + x – 32 + 90 = 180;

2x = 180 + 32 – 90;

2x = 122;

x = 122: 2;

x = 61 ° – greater acute angle of the triangle;

61 – 32 = 29 ° is the smaller acute angle of the triangle.

Answer: 29 °.