#### Question

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure |
||||

Side |
3 | 4 | 5 | 6 |

Angle sum |
180° |
2 × 180° = (4 − 2) × 180° |
3 × 180° = (5 − 2) × 180° |
4 × 180° = (6 − 2) × 180° |

What can you say about the angle sum of a convex polygon with number of sides?

a) 7

b) 8

c) 10

d) n

#### Solution

From the table, it can be observed that the angle sum of a convex polygon of *n*sides is (*n* −2) × 180º. Hence, the angle sum of the convex polygons having number of sides as above will be as follows.

(a) (7 − 2) × 180º = 900°

(b) (8 − 2) × 180º = 1080°

(c) (10 − 2) × 180º = 1440°

(d) (*n* − 2) × 180°

Is there an error in this question or solution?

Solution Examine the Table. (Each Figure is Divided into Triangles and the Sum of the Angles Deduced from That.) What Can You Say About the Angle Sum of a Convex Polygon with Number of Sides? Concept: Polygons - Convex and Concave Polygons.