In order to find the angles of a triangle, we will compose and solve an equation. It is known that one of the angles is 60 ° less than the second angle and 2 times less than the third angle.
Let us first of all recall the theorem on the sum of the angles of a triangle. It says that the sum of the angles of a triangle is 180 °.
Let’s denote by x – one of the angles, then we will write the second as (x – 60), and the third x / 2.
We get the equation:
x + x / 2 + x – 60 = 180;
x + x / 2 + x = 180 + 60;
2x + x / 2 = 240;
4x + x = 480;
5x = 480;
x = 480: 5
x = 96 ° is one of the corners, 96 – 60 = 36 ° and 96/2 = 48 °.
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