Do you use the formula:
(n-2)180 / n
to find the measure of each arc that corresponds to a side of a polygon? Example: a hexagon
(6-2))180/6 = 120 ?
Nope. 360/n corresponds to the arc subtended by each side: the central angle.
The sum of the interior angles is (n-2)*180
So, (n-2)180/n is the measure of each interior angle of the polygon.
Note that
180(n-2)/n = (180n-360)/n
= 180 - 360/n
This shows that the central angle is equal to the exterior angle. (The interior and exterior angles are supplementary.)
Let me explain. The formula (n-2)x180 is used for getting the sum of all the interior angles of a polygon and the formula (n-2)x180/n is used for getting the measure of each angle
Yes, you are correct! The formula you mentioned, (n-2)180/n, is commonly used to find the measure of each interior angle in a regular polygon. In the case of a regular hexagon (a polygon with six sides), using this formula gives us (6-2)180/6 = 4*180/6 = 720/6 = 120 degrees. Therefore, each interior angle of a regular hexagon measures 120 degrees.
Yes, you are correct! The formula you mentioned, (n-2)180/n, can be used to find the measure of each arc that corresponds to a side of a polygon.
To explain how it works, let's consider a hexagon as an example. A hexagon has six sides, so we can substitute n with 6 in the formula:
(6-2)180 / 6 = 4 * 180 / 6 = 720 / 6 = 120
Therefore, in a regular hexagon, each arc that corresponds to a side will have a measure of 120 degrees.
To understand why this formula works, we can break it down further.
The expression (n-2) gives us the number of triangles formed by drawing diagonals from each vertex of the polygon. In the case of a hexagon, we have 6 vertices, and by drawing diagonals from each vertex, we create 4 triangles.
Each triangle formed has an interior angle sum of 180 degrees. Since there are 4 triangles, the total interior angle sum for these triangles is 4 * 180 degrees.
To find the measure of a single arc, we divide the total angle sum by the number of sides of the polygon (n). This ensures that the sum of all the angles around the center of the polygon adds up to 360 degrees.
So, by dividing the total angle sum of the triangles (4 * 180 degrees) by the number of sides (6), we get 120 degrees, which represents the measure of each arc corresponding to a side of the hexagon.