In an isosceles triangle, the angle between the height to the base and the side is 18 degrees less

In an isosceles triangle, the angle between the height to the base and the side is 18 degrees less than the angle at the base. Find the angle at the base of the triangle.

We take the value of the angle at the base as x, then:

x – 18 – the value of the angle between the height and the side.

Since the height makes an angle of 90 ° with the base and the sum of the angles of the triangle is 180 °, we get the equation:

x + (x – 18) + 90 = 180;

2x – 18 = 90;

2x = 72;

x = 72: 2 = 36 °.

Answer: the required angle is 36 °.