Consecutive angles
of a parallelogram are supplementary
Consecutive angles are angles that share a common side and have a common vertex, but no other points in common. Specifically, two angles are consecutive if they are adjacent angles in a polygon.
In a polygon with n sides, the sum of the consecutive interior angles is (n-2) x 180 degrees. This formula can be used to find the measure of each consecutive angle in a regular polygon, where all angles have equal measure. To find the measure of each consecutive angle in an irregular polygon, the formula can be applied to each set of consecutive angles.
For example, consider a regular pentagon (a five-sided polygon) where all angles have equal measure. Using the formula, we can find that the sum of the consecutive interior angles is (5-2) x 180 = 540 degrees. Since there are five angles, each angle measures 540/5 = 108 degrees.
In conclusion, consecutive angles are adjacent angles that share a common side and vertex in a polygon. The sum of the consecutive interior angles can be found using the formula (n-2) x 180 degrees, where n is the number of sides in the polygon.
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