The measures of the angles in quadrilaterals are in the extended ratio of 3:4:5:6. What are the measures of the angles?

To find the measures of the angles in a quadrilateral, we first need to determine the constant multiplier for the ratios given. In this case, the extended ratio of 3:4:5:6 suggests that we have a total of 3 + 4 + 5 + 6 = 18 parts.

To find the value of each part, we divide the total sum of the parts by 18. Thus, each part is equal to 360°/18 = 20°.

Now, to find the measure of each angle, we multiply the number of parts by the value of each part in the ratio.

The angles in the given quadrilateral are:

1st angle: 3 parts * 20° = 60°
2nd angle: 4 parts * 20° = 80°
3rd angle: 5 parts * 20° = 100°
4th angle: 6 parts * 20° = 120°

Therefore, the measures of the angles in the quadrilateral are 60°, 80°, 100°, and 120°, respectively.

62:45:87:116