How do you find the sum and conjecture of a polygon?
Conjecture (Polygon Sum Conjecture): The sum of the interior angles of any convex n-gon (polygon with n sides) is given by (n-2)*180. Corollary (Angle Measures for Regular n-gons): The measure of each of the n angles in a regular n-gon is given by (n-2)*180/n.
What is the formula for polygon sum theorem?
Calculating the exterior angles of regular polygons To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.
How do you work out the number of sides of a polygon with the sum of the interior angles?
Answer: To find the number of sides of a polygon when given the sum of interior angles, we use the formula: Sum of interior angles = (n – 2) × 180, where n is the number of sides.
What is the formula for polygons?
Polygon Formula The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n.
What is the polygon exterior angle sum theorem?
If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° . The sum of the measures of the exterior angles is the difference between the sum of measures of the linear pairs and the sum of measures of the interior angles. …
What is the sum of a convex polygon?
Theorem: The sum of the angles in any convex polygon with n vertices is (n – 2) · 180°.
How many sides does a polygon have if the sum of the interior angles is 3240?
20 sides
There we go, 20 sides.
What is a polygon rule?
The sides must be straight. Polygons may have any number of sides. A polygon. A shape with curved sides is not a polygon. A shape that is not fully closed is not a polygon.
Why do the exterior angles of a polygon equal 360?
Summed, the exterior angles equal 360 degreEs. A special rule exists for regular polygons: because they are equiangular, the exterior angles are also congruent, so the measure of any given exterior angle is 360/n degrees.