Step-by-step explanation:

Given :-

A regular polygon has 18 SIDES

To find:-

i) Find the measure of its EXTERIOR angle ?

ii) Find the NUMBER of its diagonals ?

Solution :-

Given that :

The number of sides in a regular polygon (n) = 18

We know that

The measure of each exterior angle of a regular polygon of 'n' sides is 360°/n

Each exterior angle of the given regular polygon of 18 sides

=> 360°/18

=> 20°

The measure of the exterior angle = 20°

and

We know that

The number of diagonals of a regular polygon of'n'sides is n(n-3)/2

On Substituting the VALUE of n in the above formula then

=> (18)(18-3)/2

=> 18×15/2

=> 9×15

=> 135

The number of diagonlos = 135

Answer:-

I) The measure of the exterior angle of the given regular polygon = 20°

ii) The number of diagonals of the given regular polygon = 135

Used formulae:-

• The measure of each exterior angle of a regular polygon of 'n' sides is 360°/n
• The number of diagonals of a regular polygon of'n'sides is n(n-3)/2
• n = Number of sides in the given regular polygon