In a triangle, the first angle is 2 times less than the second, and the third angle is 20

In a triangle, the first angle is 2 times less than the second, and the third angle is 20 degrees less than the second. Find the corners of the triangle.

Let the angles of this triangle be A, B, C.

By the condition of the problem, the first angle is 2 times less than the second. It means:

B = 2 * A.

We also have that the third angle is 20 ° less than the second:

B = C + 20.

But the sum of the angles of the triangle is 180 °. That’s why:

A + B + C = 180 °,

A + 2 * A + B – 20 ° = 180 °,

A + 2 * A + 2 * A – 20 ° = 180 °,

5 * A = 200 °,

A = 40 °.

Then

B = 2 * A = 2 * 40 ° = 80 ° and

C = B – 20 ° = 80 ° – 20 ° = 60 °.

Answer: the angles of the triangle are 40 °, 80 °, 60 °.