write an expression for the sum of the angle measures in a regular polygan with n sides. then wirte an expression for the measure of each angle in a regular polygan with n sides.
If it has n sides you make n right turns to get all the way around the outside and end up going the same direction you were going at the start.
So each right turn is 360/n
Each interior angle is the supplement of that right turn
180 - (360/n)
so each interior angle = (180 n -360)/n
each = 180 (n-2)/n
the sum is then 180(n-2)
check that
triangle 180 (3-2)= 180 sure enough 180
square 180(4-2) = 360 yes
The expression for the sum of the angle measures in a regular polygon with n sides can be calculated using the formula:
Sum = (n - 2) * 180 degrees
This formula holds because in any polygon, the sum of the interior angles is equal to (n - 2) times 180 degrees.
To find the measure of each angle in a regular polygon with n sides, we divide the sum of the angles by the number of sides:
Measure of each angle = Sum / n
So, the expression for the measure of each angle in a regular polygon with n sides is:
Measure of each angle = ((n - 2) * 180 degrees) / n
The sum of the angle measures in any polygon can be found using the formula:
Sum of angle measures = (n - 2) * 180 degrees
Here, 'n' represents the number of sides in the polygon.
For a regular polygon, each angle measure is equal. So, to find the measure of each angle in a regular polygon with 'n' sides, we divide the sum of the angle measures by 'n':
Measure of each angle = (Sum of angle measures) / n
Therefore, the respective expressions can be written as:
1. Expression for the sum of the angle measures in a regular polygon with n sides:
Sum of angle measures = (n - 2) * 180 degrees
2. Expression for the measure of each angle in a regular polygon with n sides:
Measure of each angle = (n - 2) * 180 degrees / n