Question

24. Determine the number of sides of polygon whose exterior and interior angles are in the
ratio 1:5.​

Answer 1

Given :

• Ratio of the exterior and interior angles of the polygon = 1 : 5

To find :

• Number of sides of polygon

Concept :

To find the number of sides of the polygon :-

• Firstly, we will calculate the interior and exterior angles of the polygon. For that assume the exterior and interior angles as 1x and 5x respectively.
• By using the formula :-

➳ Interior angle + Exterior angle = 180°

• We will find the value of x and after substituting the value of x in the interior and exterior angles we will get their measure.
• To find the number of sides of the polygon, we'll use this formula :-

➳ Exterior angle = 360° ÷ n

Solution :

Let,

• Exterior angle of the polygon = 1x
• Interior angle of the polygon = 5x

Using formula,

✭ Interior angle + Exterior angle = 360°

Substituting the given values,

⇒ 1x + 5x = 360°

⇒ 6x = 360°

⇒ x = 360° ÷ 6

⇒ x = 60°

The value of x = 60°.

Substituting the value of x in the angles of the polygon :-

• Interior angle = 5x = 5 × 60° = 300°
• Exterior angle = 1x = 60°

Number of sides of the polygon :-

Using formula,

✭ Exterior angle = 360° ÷ n

Substituting the given values,

⇒ 60° = 360°/n

⇒ n = 360°/60°

⇒ n = 6

★ Number of sides of the polygon = 6

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Know More :

A regular polygon is the one in which :-

• All its sides are equal to each other.
• All its exterior angles are equal to each other.
• All its interior angles are equal to each other.

➳ Formula to calculate interior angles of a polgyon :-

• Sum of interior angles of a polygon = (2n - 4) × 90°