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 𝒃 â ĉ
The angle sum of a triangle is 180°
𝑎 + 𝑏 + 𝑐 = 180°

3. What is the angle sum of a quadrilateral?
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
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°

5. 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°

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° 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

9. 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