The angles of a convex pentagon are proportional to the numbers 1; 2; 4; 5; 6. Find these corners.

To solve this problem, recall the theorem on the sum of the angles of a polygon. The sum of the angles of an n-gon is equal to the product of 180 degrees by (n – 2). Let’s calculate what is the sum of the angles of the pentagon.

180 * (5 – 2) = 180 * 3 = 540 degrees.

Let one part be -x, then the first angle is 1 * x = x degrees, the second is 2x, the third is 4x, the fourth is 5x, the fifth is 6x. Knowing that the sum of the angles is 540 degrees, we can write the equation.

x + 2x + 4x + 5x + 6x = 540;

18x = 540;

x = 540/18;

x = 30.

The first corner – 30 g, the second – 2 * 30 = 60 g, the third – 4 * 30 = 120 g, the fourth – 5 * 30 = 150 g, the fifth – 6 * 30 = 180 g