Find the largest and smallest angles of a convex quadrilateral if they are proportional to the numbers 2: 4: 5: 7

1. Let’s denote one part by x.

2. Define the first angle of a convex quadrilateral:

2 * x = 2x.

3. Find out the degree measure of the second angle:

4 * x = 4x.

4. Determine the degree measure of the third angle:

5 * x = 5x.

5. Find out the degree measure of the fourth angle:

7 * x = 7x.

6. So the sum of the angles of a convex quadrilateral is 180˚ * (4 – 2) = 180˚ * 2 = 360˚, compose and solve the equation:

2x + 4x + 5x + 7x = 360˚

18x = 360˚;

x = 360˚: 18;

x = 20˚.

7. One part is equal to x = 20˚.

8. What is the degree measure of the first angle?

2 * x = 2 * 20˚ = 40˚.

9. What is the degree measure of the second angle?

4 * x = 4 * 20˚ = 80˚.

10. What is the degree measure of the third angle?

5 * x = 5 * 20˚ = 100˚.

11. What is the degree measure of the fourth angle?

7 * x = 7 * 20˚ = 140˚.

Answer: the angles of a convex quadrilateral are 40˚, 80˚, 100˚, 140˚.