Question

An exterior angle and an interior angle of a regular polygon are in the ratio 1:8.Find the number sides in the polygon.​

Answer 1

Answer:

• Number of sides in the polygon is 10.

Step-by-step explanation:

Given:

• Ratio of exterior angle and interior angle of a regular polygon is 1:8.

To Find:

• Number of sides in the polygon.

Solution:

Concept used:

According to the question, ratio of exterior and interior angle of polygon is given and we are said to find number of sides in the polygon so we have to assume numbers and after getting the value of x then we are eligible for find the interior and exterior angles.

Let's assume:

• Let the interior angle of the regular polygon be x.
• Let the exterior angle of the regular polygon be $\sf\dfrac{x}{4}$

As we know that,

• Sum of all sides is 180°.

Now,put the equation

Exterior angle + Interior angle = 180°

$\sf\dfrac{x}{4}$ + x = 180°

$\sf\dfrac{5x}{4}$ = 180°

x = 180° × $\sf\dfrac{4}{5}$

= 144°

• Interior angle is 144°.
• Exterior angle is 36°.

n = 360°/exterior angle

=360°/36° = 10

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