# Find the angles of an isosceles triangle if the angle at the base is 30 times greater than the angle between the sides.

From the condition, we know that we are given an isosceles triangle, and we also know that the angle at the base is 30 ° greater than the angle between the lateral sides. To find all the angles of an isosceles triangle.

Let’s remember the properties of the angles of an isosceles triangle. It says that the angles at the base of an isosceles triangle are equal.

And we also know that the sum of the angles of a triangle is 180 °.

Let us denote by the variable x the angle at the vertex, then the angle at the base is (x + 30).

Let’s compose and solve the equation:

x + 2 (x + 30) = 180;

x + 2x + 60 = 180;

3x = 180 – 60;

x = 40 ° apex angle, then base angle is 40 + 30 = 70 °.

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