Question

Q8. A student draws a regular polygon with 10 sides. He makes a design by using all the diagonals. How many diagonals he needs to draw also find each interior angle of the polygon?

Answer 1

Answer:

Number of diagonals of a decagon = 35

each interior angle = 144°

Step-by-step explanation:

Number of diagonals of a polygon = {n (n - 3) } ÷ 2

where n = Number of sides of a polygon

For a decagon,

n = 10,

Number of diagonals = {10 (10 - 3) } ÷ 2

= (10 * 7) ÷ 2

= 70 ÷ 2 = 35

Each interior angle of a polygon = {( n - 2) * 180°} ÷ n

where n= Number of sides of a polygon

For n = 10,

Each interior angle = { (10 - 2) * 180 } ÷ 10

= (8 * 180) ÷ 10

= 1440 ÷ 10 = 144°