The angles of the triangle form a geometric progression. If the smaller angle is 20 degrees

The angles of the triangle form a geometric progression. If the smaller angle is 20 degrees, then the denominator of the progression is?

The sum of the angles of any triangle is 180 °. The problem comes down to finding the denominator of a geometric progression by the known sum of its three first terms and the first term 20.

S3 = b1 * (1 – q ^ 3) / (1 – q).

180 = 20 * (1 – q) (1 + q + q ^ 2) / (1 – q).

180/20 = 1 + q + q ^ 2.

Let’s solve the quadratic equation.

q ^ 2 + q – 8 = 0;

D = 1 * 1 + 4 * 8 = 1 + 32 = 33.

q = (- 1 + √33) / 2.

Answer: the denominator of the progression is (√33 – 1) / 2.