Angles and Polygons
Polygon problems use angle relationships to find missing values and classify shapes.
Angle facts
Angles on a straight line sum to 180°, angles around a point sum to 360°, and vertically opposite angles are equal. A polygon with n sides has interior-angle sum (n−2) × 180°. For a regular polygon, each interior angle is ((n−2) × 180°)/n.
Worked examples
- Each interior angle of a regular pentagon is (5−2) × 180° ÷ 5 = 108°.
- The exterior angle of a regular hexagon is 360° ÷ 6 = 60°.
- If adjacent angles on a line are x and 2x, then 3x = 180°, so x = 60°.
Practice
- Find the interior-angle sum of a nonagon.
- Find each angle of a regular octagon.
- Solve for x when angles around a point are 90°, 120° and x.
