Find the sharp corners of a right triangle if one of them is a quarter of the other.

We are given a right-angled triangle, and we also know that one of the acute angles of the triangle is 1/4 of the other.

In order 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 using the variable x °, then the second can be written as 1 / 4x °.

Let’s solve the equation:

x + 1 / 4x + 90 = 180;

5 / 4x = 180 – 90;

5 / 4x = 90;

x = 72 °.

So, one of the acute angles is 72 °, and the second 1/4 * 72 = 18 °