In an isosceles triangle, the apex angle is 2.5 times less than the base angle.

In an isosceles triangle, the apex angle is 2.5 times less than the base angle. Express the angles of a triangle in degrees and radians (in fractions of π) measures.

It is known from the condition that in an isosceles triangle the angle at the apex is 2.5 times less than the angle at the base. In order to find all the angles of a triangle, first of all, let’s 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 °.

Since the triangle is isosceles, the angles at its base are equal. Let’s designate the angles at the base using the variable x, then we can write the angle at the top as 2.5x.

Let’s compose and solve the equation:

x + x + 2.5x = 180;

4.5x = 180;

x = 180 / 4.5;

x = 40 ° equal angles at the base, 40 * 2.5 = 100 ° angle at the top.