Question

In a regular polygon of n sides, each interior angle is 5 times the exterior angle. Find n

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Answer 1

Hola user !!!!

Answer:

12

Explanation:

The exterior angles of a dodecagon are 30 so they sum to 12×30=360

The interior angles are 150=180−30=5×30



Answer:

We need to be able to calculate this, without having to consider the size of the exterior and interior angles of all the different polygons.

Explanation:

Let the size of an exterior angle be x°
The size of the interior angle is therefore 5x°

An exterior and interior angle are supplementary angles.

x°+5x°=180°⇒6x=180°

x=30° This is size of each exterior angle (ext∠)

The sum of the exterior angles is 360°

Number of sides (or angles) = 360ext∠ 
36030=12 sides


hope this clarifies.....!!!!

Answer 2

Let the exterior angle be 'x'.

Given that Each interior angle is 5 times the exterior angle.

We know that exterior angle + interior adjacent angle = 180

⇒ x + 5x = 180

⇒ 6x = 180

⇒ x = 180/60

⇒ x = 30.

Now,

We know that sum of exterior angles of any polygon = 360.

⇒ Number of sides n = (360/exterior angle)

⇒ n = (360/x)

⇒ n = (360/30)

⇒ n = 12.

Therefore, the number of sides = 12.

Hope it helps!