The perimeter of the parallelogram is 66 cm. The two corners of the parallelogram are 1: 5

The perimeter of the parallelogram is 66 cm. The two corners of the parallelogram are 1: 5 and the two sides are 2: 9. Find the sides and angles of the parallelogram.

1. Let’s denote one part by x.

2. Let us determine the degree measures of the angles of the parallelogram:

x and 5x.

3. Let’s compose and solve the equation:

5x + x = 180˚;

6x = 180˚;

x = 180˚: 6;

x = 30˚.

4. The degree measure of the smaller angle is 30˚.

5. What is the degree measure of the larger angle?

5 * 30˚ = 150˚.

6. Let’s define the sides of the parallelogram:

2x and 9x cm.

7. Let’s compose and solve the equation:

(2x + 9x) * 2 = 66;

11x = 66: 2;

11x = 33;

x = 33: 11;

x = 3.

8. One part is equal to 3.

9. What is the smaller side of the parallelogram?

2 * 3 = 6 cm.

10. How long is the longer side of the parallelogram?

9 * 3 = 27 cm.

Answer: the angles of the parallelogram are 30˚, 150˚, 30˚, 150˚, and the sides of the parallelogram are 6 cm, 27 cm, 6 cm, 27 cm.