Find the acute angle of a right-angled triangle if one is 8 times smaller than the others.

A right-angled triangle is given, and it is also known that one of the acute angles of the triangle is 8 times smaller than the other.

To find the acute angles of a triangle, let us first recall the theorem on the sum of the angles of a triangle. It says that the sum of the angles of the triangle is 180 °.

Let’s designate one of the acute angles of the triangle with the variable x °, then the second can be written as 8x °.

Let’s solve a linear equation with one variable:

x + 8x + 90 = 180;

9x = 180 – 90;

9x = 90;

x = 10 °.

So, one of the acute angles is 10 °, and the second 8 * 10 = 80 °