Question

write a program that inputs the number of sites of polygon and then determined whether it is hexagon, a Pentagon, a rectangle, or a triangle.

Answer 1

We will learn how to find the sum of the interior angles of a polygon having n sides.

We know that if a polygon has ‘n’ sides, then it is divided into (n – 2) triangles. 

We also know that, the sum of the angles of a triangle = 180°.

Therefore, the sum of the angles of (n – 2) triangles = 180 × (n – 2)

                                                                            = 2 right angles × (n – 2)

                                                                            = 2(n – 2) right angles

                                                                            = (2n – 4) right angles

Therefore, the sum of interior angles of a polygon having n sides is (2n – 4) right angles.

Thus, each interior angle of the polygon = (2n – 4)/n right angles.

Now we will learn how to find the find the sum of interior angles of different polygons using the formula.

Name

Figure

Number of Sides

Sum of interior angles (2n - 4) right angles

Triangle



3

(2n - 4) right angles

= (2 × 3 - 4) × 90°

= (6 - 4) × 90°

= 2 × 90°

= 180°

Quadrilateral



4

(2n - 4) right angles

= (2 × 4 - 4) × 90°

= (8 - 4) × 90°

= 4 × 90°

= 360°

Pentagon



5

(2n - 4) right angles

= (2 × 5 - 4) × 90°

= (10 - 4) × 90°

= 6 × 90°

= 540°

Hexagon



6

(2n - 4) right angles

= (2 × 6 - 4) × 90°

= (12 - 4) × 90°

= 8 × 90°

= 720°

Heptagon



7

(2n - 4) right angles

= (2 × 7 - 4) × 90°

= (14 - 4) × 90°

= 10 × 90°

= 900°

Octagon



8

(2n - 4) right angles

= (2 × 8 - 4) × 90°

= (16 - 4) × 90°

= 12 × 90°

= 1080°