In an isosceles triangle, the apex angle is 2.5 times less than the base angle.

In an isosceles triangle, the apex angle is 2.5 times less than the base angle. Find the angles of the triangle and express them in degrees and radians.

Let the angle at the apex of an isosceles triangle be x, then the angles at the base of this triangle will be 2.5x (in an isosceles triangle, the angles at the base are equal).
Since the sum of the angles of the triangle is 180 °, we get the equation:
x + 2.5x + 2.5x = 180 °
6x = 180 °
x = 30 ° – apex angle.
2.5x = 2.5 * 30 = 75 ° – one of the two angles at the base.
Let us express the found angles in radians.
1 ° = ╥ / 180 radians, respectively, we get:
30 ° = ╥ / 60 radians – apex angle;
75 ° = 5╥ / 12 radians is one of the two base angles.
Answer: the base angle is 30 ° or ╥ / 60 radians, one of the base angles is 75 ° or 5╥ / 12 radians.