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The formula for the sum of that polygons interior angles is refreshingly simple.
Find the measure of each interior and exterior angle. For n16 interior angle will have measure 16-2180161575 and exterior angle will have measure 36016225. Each Interior angle of a polygon n 1 8 0 o n 2 Each Exterior angle of a polygon n 3 6 0 o n 1 8 0 o n 2 5 n 3 6 0 o n 2 1 0 n 1 2 Number of sides of polygon is 12. 360 n.
Using our new formula any angle n 2 180 n For a triangle 3 sides 3 2 180 3 1 180 3 180 3 60. Therefore the exterior angle of a. Here is the formula.
The measure of each internal angle in a regular polygon is found by dividing the. As each of the exterior angles are equal Exterior angle 360 15 24. Measure of one exterior angle 3609 40 Measure of one interior angle 180929 140.
You might already know that the sum of the interior angles of a triangle measures 180 and that in the special case of an equilateral triangle each angle measures exactly 60. For a pentagon the number of sides is 5 which we can substitute in the formula to get -. The measure of each exterior angle 360n where n number of sides of a polygon.
Therefore we can subtract the interior angle from 180 to find the measure of the exterior angle. Mathematics RS Aggarwal 2016 Standard VIII. Hence Sum of the exterior angles of any polygon is.
One important property about a regular polygons exterior angles is that the sum of the measures of the exterior angles of a. For a regular n-agon the measure of an exterior angle is 360n. Measure of each interior angle of an n-sided regular polygon 180 n-2n.
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