Angles in polygons
The interior angles of a polygon with n sides add up to (n - 2) x 180 degrees. The outside (exterior) angles always add up to 360 degrees.
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Analogy
Like cutting a shape into triangles from one corner, each worth 180 degrees.
Example
Sum = (6 - 2) x 180 = 720Each angle = 720 / 6 = 120Exterior = 360 / 6 = 60
In practice
Floor tilers need to know a hexagon's angle is 120 degrees so tiles fit without gaps.
Practice
Flashcards
- What is the sum of interior angles in a hexagon?720 degrees, from (6 - 2) x 180.
Interview questions
- Calculate the interior angle of a regular hexagon and explain your method.
- A hexagon splits into 4 triangles
- Sum of angles = 4 x 180 = 720
- Divide by 6 equal angles
- Each angle is 120 degrees
Questions people ask
Why is the sum (n - 2) x 180 degrees?
From one corner, you can draw lines to split any polygon into n - 2 triangles. Each triangle has angles adding to 180 degrees. A hexagon has 6 sides, so it splits into 4 triangles, giving 4 x 180 = 720 degrees in total.
What is a regular polygon?
A regular polygon has all sides the same length and all angles the same size. A square and an equilateral triangle are regular. A rectangle is not, because its sides are not all equal. In a regular polygon each exterior angle is 360 divided by n.