In this formula, n is the number of sides of the polygon.
The formula tells you what the interior angles of a polygon add up to.
How to Find the Sum of the Interior Angles of a Polygon
Finding the sum of the interior angle of a polygon is easy.Question
What is the sum of the interior angles of a pentagon?
Step-by-Step:
1
Start with the formula:
Sum of interior angles = (n − 2) × 180°
2
Substitute the number of sides into the formula.
A pentagon has 5 sides. In our example, n = 5.
Sum of interior angles = (5 − 2) × 180°
Sum of interior angles = 3 × 180°
Sum of interior angles = 540°
Answer:
The sum of the interior angles of a pentagon is 540°.What Are the Interior Angles of a Polygon?
The interior angles of a polygon are the angles between two sides, inside the shape.Why Does the Formula Work?
Any polygon can be split into a number of triangles, each of which has interior angles adding up to 180°.
The number of triangles is 2 less than the number of sides and there are there are 180° of interior angles for every triangle:
(n − 2) × 180°
This is why the formula works.
This page was written by Stephen Clarke.
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geometryfinding the interior angle of a regular polygonunderstanding the exterior angles of a polygonfinding the exterior angle of a regular polygon
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