Question

If the sum of the interior angles of a regular polygon is 1440°. Find the number of sides of the polygon also find its each exterior angle.​

Answer 1

Given:-

Sum of all interior angles of polygon = 1440°

Formula Used:-

The sum of all interior angles of a polygon = (n-2) × 180°

where n = no. of sides

Calculation:-

The sum of all interior angles of a polygon = (n-2) × 180°

⇒ 1440° = (n-2) × 180°

⇒ (1440°/180°) = (n-2)

⇒ 8 = n-2

⇒ n = 10

Answer 2

Answer:

Step-by-step explanation:

given s=1440 degrees

S=(n-2)*180

1440=(n-2)*180

1440/180=(n-2)

8=(n-2)

8+2=n

10=n

therefore, number of sides of polygon, n=10

one interior angle = 1440/10=144  degrees

since it is regular( decagon) all interior angles are same

therefore, each exterior angle = (180 degree - 144 degree)=36 degrees

or

since it is regular polygon, you can find each exterior angle using eqn

360/n = 360/10=36 degrees