Find the angle at the base of an isosceles triangle if the apex angle is 4 times less than the base angle.

1. In an isosceles triangle, the angles at the base are equal. Take one of these angles at the base as X. Then the second angle at the base will also be equal to X.
2. We know that if the apex angle is 4 times less than the base angle. We designated the angle at the base as X, which means that the angle at the top is X / 4
3. The sum of the angles in any triangle = 180 degrees. Let’s make an equation, adding all the angles, and solve it:
X + X + X / 4 = 180
2X + X / 4 = 180
Now we multiply both sides of the equation by 4 to get rid of the fraction:
8X + X = 720
9X = 720
Hence X = 720: 9 = 80 degrees.
The answer is the angle at the base is 80 degrees.