1. Interior angles of polygons This is just one of the six interior angles of this polygon

2. The angle sum of a triangle is 180° A polygon with 3 sides is a triangle âĉ

3. What is the angle sum of a quadrilateral? Angle sum of a triangle = 180° Angle sum of a triangle = 180° The angle sum of a quadrilateral is 360°

4. Here is a different quadrilateral but the method is the same Angle sum of a triangle = 180° Angle sum of a triangle = 180° The angle sum of a quadrilateral is 360° The formula applies for any polygon, not just regular polygons!

5. What is the angle sum of a pentagon? This time you can divide the polygon into 3 triangles 3 x 180°= 540° The angle sum of a pentagon is 540°

6. You can find the angle sum of any polygon by dividing it up into triangles 4 x 180° = 720° 5 x 180° = 900° 6 x 180° = 1080°

7. Using the formula (n-2) x 180° Find the angle sum for a dodecagon (a 12-sided polygon) (12-2) x 180°= 10 x 180°= 1800°

8. EXAMPLES 1) 2) 95° 155° 80° 120° 110° 120° 95° 105° Pentagon (5 sides) Sum of interior angles = (number of sides – 2)x 180° Sum of interior angles = ( 5 – 2 )x 180° Sum of interior angles = 3 x 180° Sum of interior angles = 540° - 90° - 155° - 95° - 80° Hexagon (6 sides) Sum of interior angles = (number of sides – 2)x 180° Sum of interior angles = ( 6 – 2 )x 180° Sum of interior angles = 4 x 180° Sum of interior angles = 720° - 120° - 110° - 120° - 95° - 105° L.O. To be able to use the formula

9. The sum of interior angles for any polygon 4. Find the missing angles a) b) 1. Work out the sum of the interior angles of a heptagon 2. Work out the sum of the interior angles of a nonagon (9 sides) 3. Work out the sum of the interior angles of a 14-sided polygon