Finding the Sum of the Interior Angles of a Polygon
(KS2, Year 6)
The LessonThe sum of the interior angles of a polygon is found using the formula:
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 PolygonFinding the sum of the interior angle of a polygon is easy.
QuestionWhat is the sum of the interior angles of a pentagon?
Start with the formula:
Sum of interior angles = (n − 2) × 180°
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°.
Lesson SlidesThe slider below shows another real example of how to find the sum of the interior angles of a polygon. Open the slider in a new tab
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.
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