Find the sharp corners of a rectangle of a triangle if one is 4 times the size of the other

We are given a right-angled triangle, and we also know that one of the acute angles of the triangle is 4 times larger than 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 4x °.

Let’s solve the equation:

x + 4x + 90 = 180;

5x = 180 – 90;

5x = 90;

x = 18 °.

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