In an isosceles triangle, the angle at the base is 64 degrees, find the remaining angles.

It is known from the condition that in an isosceles triangle the angle at the base is 64 °. In order to find the rest of the angles, recall and apply 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 us also recall the property of angles at the base of an isosceles triangle. The angles at the base of an isosceles triangle are equal to each other.

So we know the degree measure of two angles at the base. Find the third corner of the triangle:

180 ° – (64 ° + 64 °) = 180 ° – 128 ° = 52 ° apex angle.