Find the angle at the base of an isosceles triangle if the angle between the sides is 80 degrees.

Let us take advantage of the fact that the sum of all the internal catch of any triangle is always 180 °, as well as the fact that every isosceles triangle has the same angles at the base.

Let us denote by x the value of one of the catch at the base in a given isosceles triangle.

Then the value of the other angle at the base of this triangle will also be equal to x.

Since the apex angle is 80 °, we can write the following equation:

x + x + 80 = 180,

solving which, we get:

2x + 80 = 180;

(2x + 80) / 2 = 180/2;

x + 40 = 90;

x = 90 – 40;

x = 50 °.

Answer: 50 °.