What is the measure of each angle in a hexagon if all angles are congruent?
If all angles in a hexagon are congruent, it means that each angle has the same measure. To find the measure of each angle, we can divide the sum of the angles in a hexagon by the number of angles.
In a hexagon, the sum of the interior angles is given by the formula:
Sum = (n - 2) * 180 degrees
where n is the number of sides of the polygon.
For a hexagon, n = 6. Thus,
Sum = (6 - 2) * 180 degrees = 4 * 180 degrees = 720 degrees.
Since all angles in the hexagon are congruent, we divide the sum by the number of angles to find the measure of each angle:
Measure of each angle = Sum / n
= 720 degrees / 6
= 120 degrees.
Therefore, the measure of each angle in a hexagon if all angles are congruent is 120 degrees.