Angles in Polygons
What's a Polygon?
A polygon is a 2D shape with straight sides.
Examples: triangle, square, pentagon, hexagon, etc.
Total Interior Angles Formula:
To find the sum of the interior angles in a polygon:
(n − 2) × 180°
Where n is the number of sides.
Example:
A hexagon has 6 sides. => (6 − 2) × 180 = 4 × 180 = 720°
So, all the inside angles of a hexagon add up to 720°.
Each Interior Angle (if regular):
If the polygon is regular (all sides and angles are equal), divide the total by the number of sides:
Interior angle = ((n − 2) × 180) ÷ n
Example:
Regular pentagon → 5 sides : ((5 − 2) × 180) ÷ 5 = (3 × 180) ÷ 5 = 540 ÷ 5 = 108°
So, each interior angle is 108°.
Total Exterior Angles:
Exterior angles are the angles you get when you extend a side of the polygon.
Sum of all exterior angles = ALWAYS 360°
Each Exterior Angle (if regular):
Exterior angle = 360 ÷ n
Examples
Example 1 : Find angle x.
Answer:
Example 1 : Find angle y.
Answer:
Top Tips:
🔸 For interior angle sums, use: (n − 2) × 180
🔸 For each interior angle in a regular polygon: Divide the total by n
🔸 Exterior angles always add up to 360°
🔸 Interior + exterior angle at a corner = 180°
🔸 Remember: regular = all sides and angles equal