Question

Draw any four polygon. Find sum of interior angles of it. Verify 'sum of interior angles of polygon =(n_2) ×180 where n is number of sides of polygon.'​

Answer 1

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°

Answer 2

Find the ratio in which X-axis divides the segment joining A (3, -2) and B (-6, 4) from B.