Find the angles of the convex hexagon if they are proportional to the numbers 2,4,4,6,8,12.

1. Let’s denote one part by x.

2. Define the first angle of the convex hexagon

2 * x = 2x.

3. Find out what the second angle of the convex hexagon is equal to:

4 * x = 4x.

4. Define the third angle of the convex hexagon

4 * x = 4x.

5. Write down the fourth angle of the convex hexagon

6 * x = 6x.

6. Find out what the fifth angle of the convex hexagon is equal to

8 * x = 8x

7. Determine the sixth angle of the convex hexagon

12 * x = 12x.

8. Let’s compose and solve the equation:

2x + 4x + 4x + 6x + 8x + 12x = 180˚ * (6 – 2);

36x = 720˚;

x = 720˚: 36;

x = 20˚.

9. The first angle of the convex hexagon is 2 * x = 2 * 20˚ = 40˚.

10. What is the second angle of the convex hexagon?

4 * x = 4 * 20˚ = 80˚

11. What is the third angle of a convex hexagon?

4 * x = 4 * 20˚ = 80˚

12. What is the fourth angle of a convex hexagon?

6 * x = 6 * 20˚ = 120˚

13. What is the fifth angle of a convex hexagon?

8 * x = 8 * 20˚ = 160˚

14. What is the sixth angle of a convex hexagon?

12 * x = 12 * 20˚ = 240˚

Answer: The angles of the convex hexagon are 40˚, 80˚, 80˚, 120˚, 160˚, 240˚.