Given that the exterior angle of a regular hexagon is x, find the size of each interior angle of hexagon.
have you ever looked at a polygon?
The interior angles and the exterior angles are supplementary!
And, the sum of all the exterior angles is 360°
To find the size of each interior angle of a regular hexagon, we start by noting that the sum of the interior angles of any polygon can be found using the formula:
Sum of interior angles = (n - 2) * 180 degrees
where "n" represents the number of sides of the polygon.
In the case of a regular hexagon, which has six sides, we substitute "n" with 6:
Sum of interior angles = (6 - 2) * 180 degrees
= 4 * 180 degrees
= 720 degrees
Since a hexagon has six interior angles, we can find the size of each interior angle by dividing the sum of the interior angles by the number of angles:
Size of each interior angle = Sum of interior angles / Number of angles
= 720 degrees / 6
= 120 degrees
Therefore, each interior angle of a regular hexagon is 120 degrees.