Question

Find the number of sides of a polygon whose exterior and interior angles are in the ratio 1:5

Answer 1

Answer:

Given ratio of exterior and interior angle of polygon 1:5. Then, exterior angle is 16×1800and interior angle is 56×1800. =360030=12.

Step-by-step explanation:

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Answer 2

Answer :-

The number of sides of polygon is 12.

Step-by-step explanation:

To Find :-

• The number of sides of the polygon.

★ Solution

Given that,

• The exterior angle and Interior angle of a regular polygon = 1:5

Let us assume the ratio exterior angle and Interior angle of the polygon as 1x and 5x respectively.

• ∴ 1x + 5x = 180°

⇒ 1x + 5x = 180

⇒ 6x = 180

⇒ x = 180/6

⇒ x = 30

We got, The value of x is 30.

The exterior and interior angles are :-

• 1x = 1*30 = 30° ... exterior angle
• 5x = 5*30 = 150° ... interior angle

Now, According the question,

• The number of sides are :-

⇒ 360/Measure of interior angle

⇒ 360/30

⇒ 36/3

⇒ 12 sides

Hence, Number of side of the regular polygon is 12 sides.