Prove that the sum of the angles of a right-angled triangle is 90 degrees.

Let us denote the acute angles of a right-angled triangle through α and β.

According to the condition of the problem, this triangle is right-angled, therefore, the value of the third angle of this triangle is 90 °.

Since the sum of the values of all the angles of any triangle is always 180 °, we can write the following relationship:

α + β + 90 = 180,

from which follows:

α + β + 90 – 90 = 180 – 90;

α + β = 90 °.

Therefore, the sum of the acute angles of any right triangle is always 90 °.