In an isosceles triangle, the base angle is 15 degrees greater than the apex angle Find the angles of the triangle.

In an isosceles triangle, the angles adjacent to the base are equal.

Each of these two angles is 15˚ larger than the third angle (at the apex).

It is known that the sum of all the angles of a triangle is 180˚.

Let’s designate the value of the angle at the vertex X (x). Then the sum of the angles will be:

X + (X + 15) + (X + 15) = 180

We transform and solve.

3X + 30 = 180

3X = 180 – 30

3X = 150

X = 150/3

X = 50

We found the angle at the top: 50˚.

Therefore, the angle at the base is

50˚ + 15˚ = 65˚

Check: 50˚ + 65˚ + 65˚ = 180˚ (correct)

Answer: The angles of this triangle are 50˚, 65˚ and 65˚.