Angle Sum of A Convex Polygon
A polygon has many sides, a regular polygon has all sides the same length and each angle the same size.
Examples:
![Picture](/uploads/2/3/4/0/23408802/9734691.png)
1. Both shapes on the right are polygons, one is regular and the other is irregular. They both have 6 sides. Figure out which polygon is the regular one and why.
Solution
The polygon on the right is the regular pentagon because its sides are all equal.
Solution
The polygon on the right is the regular pentagon because its sides are all equal.
![Picture](/uploads/2/3/4/0/23408802/8810674.png)
2. Find the angle sum of a octagon.
Solution
An octagon can be divided into six triangles by
drawing the diagonals from one vertex.
The total of the angles in an octagon = 180° × 6
= 1080°
*same goes with other polygons, e.g. a hexagon would have 4 triangles*
Solution
An octagon can be divided into six triangles by
drawing the diagonals from one vertex.
The total of the angles in an octagon = 180° × 6
= 1080°
*same goes with other polygons, e.g. a hexagon would have 4 triangles*
The angle sum of a convex polygon with n sides is given by the formula A = 180(n − 2)°.
![Picture](/uploads/2/3/4/0/23408802/6769540.jpeg)
3. Find the angle sum of a pentagon
Solution
*A pentagon has 5 sides (n)*
A = 180(5 − 2)
= 180 × 3
= 540°
∴ The angle sum of a pentagon is 540°.
Solution
*A pentagon has 5 sides (n)*
A = 180(5 − 2)
= 180 × 3
= 540°
∴ The angle sum of a pentagon is 540°.
![Picture](/uploads/2/3/4/0/23408802/8237979.jpg)
4. Find the size of the missing angle in this shape.
Solution
The shape is a pentagon (n = 5).
Angle sum of a pentagon = 180° × (5 − 2)
= 180° × 3
= 540°
*k represented to be the unknown angle*
100° + 140° + 140° + 110° + k = 540°
k° = 50°
Solution
The shape is a pentagon (n = 5).
Angle sum of a pentagon = 180° × (5 − 2)
= 180° × 3
= 540°
*k represented to be the unknown angle*
100° + 140° + 140° + 110° + k = 540°
k° = 50°
![Picture](/uploads/2/3/4/0/23408802/7575714.png)
5.Find the size of one angle in a regular hexagon.
Solution
A hexagon has six sides (n = 6).
180°(6 − 2) = 180° × 4
= 720°
Angle sum of a hexagon = 720°
For a regular hexagon: x° = 720° ÷ 6
x° = 120°
∴ Each angle in a regular hexagon is 120°.
Solution
A hexagon has six sides (n = 6).
180°(6 − 2) = 180° × 4
= 720°
Angle sum of a hexagon = 720°
For a regular hexagon: x° = 720° ÷ 6
x° = 120°
∴ Each angle in a regular hexagon is 120°.
Quiz
1. Which of the polygons below is a heptagon?
2. Complete the table below:
3. Find the sum of the interior angles in:
a. a 15-agon b. a 20-agon c. a 50-agon d. a 100-agon
4. Find the number of sides of the polygon if the total number of degrees of the interior angles is:
a. 3460° b. 5760° c. 8320° d. 9640°
5. Find the angles marked by the pronumerals in these polygons:
a. a 15-agon b. a 20-agon c. a 50-agon d. a 100-agon
4. Find the number of sides of the polygon if the total number of degrees of the interior angles is:
a. 3460° b. 5760° c. 8320° d. 9640°
5. Find the angles marked by the pronumerals in these polygons: