Question

The ratio between the exterior angle & the interior angle of a regular polygon is 1:4. Find (i) each exterior

angle, (ii) the number of sides in the polygon​

Answer 1

Answer :

Each exterior angle = 36°

The number of sides in the polygon = 10 sides

Explanation :

We are given :

• Ratio between the exterior angle and the interior angle of a regular polygon = 1 : 4

Need to find :

• Each exterior angle
• Number of sides in the polygon

Solution :

Let us assume that :

• Exterior angle of the polygon = 1x
• Interior angle of the polygon = 4x

Using formula,

→ Interior angle + Exterior angle = 180°

Substituting the given values :

→ 1x + 4x = 180°

→ 5x = 180°

→ x = 180°/5

→ x = 36°

Substituting the value of x in the exterior angle and the interior angle $:$

→ Exterior angle = 1x

→ Exterior angle = 36°

→ Interior angle = 4x

→ Interior angle = 4(36°)

→ Interior angle = 144°

Now, calculating the number of sides of the polygon :

Using formula,

→ Each exterior angle = 360°/n

where,

• n denotes the number of sides

Substituting the given values :

→ 36° = 360°/n

→ n = 360°/36°

→ n = 10

Therefore, the number of sides in the polygon = 10 sides

Answer 2

Answer:

Each exterior angle = 36°

The number of sides in the polygon = 10 sides

Explanation :

We are given :

Ratio between the exterior angle and the interior angle of a regular polygon = 1 : 4

Need to find :

Each exterior angle

Number of sides in the polygon

Solution :

Let us assume that :

Exterior angle of the polygon = 1x

Interior angle of the polygon = 4x

Using formula,

→ Interior angle + Exterior angle = 180°

Substituting the given values :

→ 1x + 4x = 180°

→ 5x = 180°

x = 180°/5

→ x = 36°

Substituting the value of x in the exterior angle and the interior angle ::

→ Exterior angle = 1x

→ Exterior angle = 36°

→ Interior angle = 4x

→ Interior angle = 4(36°)

→ Interior angle = 144°

Now, calculating the number of sides of the polygon :

Using formula,Each exterior angle = 360°/n

where,

n denotes the number of sides

Substituting the given values :

→ 36° = 360°/n

→ n = 360°/36°

→ n = 10

Therefore, the number of sides in the polygon = 10 sides. hope it helps you g ❤️