Question

find the number of sides in a polygon if the ratio between an exterior and interior angle is 2:1

Answer 1

• The number of sides in a polygon is 6 sides .

Explanation :-

Given that,

The ratio between exterior and interior angle of a polygon is 2:1

Assumption

Let us assume the exterior angle and interior angle as 2x and 1x respectively.

As we know that,

Exterior angle + interior angle = 180°

Finding, the value of x :-

→ 2x + 1x = 180

→ 3x = 180

→ x = 180/3

→ x = 60

The value of x is 60.

ㅤㅤ∴ The exterior angle of polygon = 60°

Now, According the question,

• Number of sides in a polygon :-

We know,

Exterior angle = 360°/n

Where,

n = Number of sides.

Therefore,

→ 60 = 360/n

→ 60n = 360

→ n = 360/60

→ n = 36/6

→ n = 6

Hence, Number of sides in a polygon is 6 sides.