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

The angle sum of a triangle is 180° A polygon with 3 sides is a triangle 𝒃 â ĉ The angle sum of a triangle is 180° 𝑎 + 𝑏 + 𝑐 = 180°

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

Here is a different quadrilateral but the method is the same The formula applies for any polygon, not just regular polygons! 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°

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

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°

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°

EXAMPLES 1) 2) - - - - - - - - - 95° 155° 80° 120° 110° 95° 105°   2) 120° 110° 95° 105°   Pentagon (5 sides) Hexagon (6 sides)     Sum of interior angles = (number of sides – 2) x 180° Sum of interior angles = (number of sides – 2) x 180° Sum of interior angles = ( 5 – 2 ) x 180° Sum of interior angles = ( 6 – 2 ) x 180° Sum of interior angles = 3 x 180° Sum of interior angles = 4 x 180° Sum of interior angles = 540° Sum of interior angles = 720°   - - - -   - - - - - 90° 155° 95° 80° 120° 110° 120° 95° 105°     8

The sum of interior angles of any polygon 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 4. Find the missing angles b) a) tetradecagon