Find the angle at the base of an isosceles triangle if the angle at its apex is 70.

The ABC triangle is isosceles if the sides are equal to each other

| AB | = | BC |

and, accordingly, the angles at the base are equal:

A ̂ = C ̂

As you know, the sum of the interior angles of a triangle is 180 degrees:

A ̂ + B ̂ + C ̂ = 180

By the condition of the problem:

B ̂ = 70

Then:

A ̂ + 70 + C ̂ = 180;

A ̂ + C ̂ = 110;

A ̂ + C ̂ = 2A ̂ = 2C ̂ = 110;

A ̂ = C ̂ = 55.

Answer: The angle at the base of an isosceles triangle is 55 degrees.