The measures of the angles of the quadrilateral are in the ratio of 2:4:6:8, Find the measure of each angle.
Total degrees = 360º
2+4+6+8 = 20
Divide 360º by 20, then multiply by various ratios.
To find the measure of each angle in the quadrilateral, we need to determine the value of the common ratio. Given that the angles are in the ratio of 2:4:6:8, we add up the ratios to get the sum of the measures: 2 + 4 + 6 + 8 = 20.
Next, we divide each ratio by the sum of the measures to find the value of the common ratio:
- For the first angle, 2 / 20 = 0.1.
- For the second angle, 4 / 20 = 0.2.
- For the third angle, 6 / 20 = 0.3.
- For the fourth angle, 8 / 20 = 0.4.
Now that we have the values of the ratios, we multiply each ratio by 360 degrees (the sum of the interior angles of a quadrilateral) to find the measure of each angle:
- The measure of the first angle: 0.1 * 360 = 36 degrees.
- The measure of the second angle: 0.2 * 360 = 72 degrees.
- The measure of the third angle: 0.3 * 360 = 108 degrees.
- The measure of the fourth angle: 0.4 * 360 = 144 degrees.
Therefore, the measure of each angle in the quadrilateral is 36 degrees, 72 degrees, 108 degrees, and 144 degrees.