Math, asked by sharjeelzahid263, 2 months ago

12. The ratio of an interior angle to an exterior angle of an n-sided regular polygon is 13:2. Find the value of n.
of its exterior angles, find the​

Answers

Answered by tennetiraj86
8

Step-by-step explanation:

Given:-

The ratio of an interior angle to an exterior angle of an n-sided regular polygon is 13:2.

To find:-

Find the value of n. and Find its exterior and interior angles

Solution:-

The ratio of an interior angle to an exterior angle of an n-sided regular polygon is 13:2.

We know that the interior angle of an n-sided polygon = [(n-2)/n]×180°

We know that the exterior angle of an n-sided polygon = 360°/n

Thier ratio = [(n-2)/n]×180° : (360°/n)

=>(n-2)×180°/n : 360°/n

=>(n-2)/n : 2/n

=>(n-2) : 2

According to the given problem

The ratio is 13:2

=>(n-2) : 2 = 13:2

=>(n-2)/2 = 13/2

On applying cross multiplication then

=>(n-2)×2 = 13×2

=>2n-4 = 26

=>2n = 24+6

=>2n = 30

=>n=30/2

=>n = 15

The exterior angle = 360°/15 = 24°

The interior angle = (15-2)×180°/15

=>13×180°/15

=>13×12°

=>156°

Answer:-

The value of n = 15

The exterior angle of the polygon = 24°

The interior angle of the polygon = 156°

Used formulae:-

  • an exterior angle of an n-sided regular polygon is 360°/n
  • an interior angle of an n-sided regular polygon is [(n-2)/n]×180°
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