Question

The ratio of an interior angle to the exterior angle of a regular polygon is 5:1. Find the number of sides.​

Answer 1

Answer:

It has 12 sides.

Step-by-step explanation:

From the question it is given that, The ratio between an exterior angle and the interior angle of a regular polygon is 1: 5

Let us assume exterior angle be y And interior angle be 5y

We know that, sum of interior and exterior angle is equal to 180∘,

y+5y=180∘6y=180∘y=180∘/6y=30∘

the number of sides in the polygon The number of sides of a regular polygon whose each interior angles has a measure of

150∘

Let us assume the number of sides of the regular polygon be n,

Then, we know that 150∘=((2n−4)/n)×90∘

150∘/90∘=(2n−4)/n5/3=(2n−4)/n

By cross multiplication,3(2n−4)=5n

6n−12=5n

By transposing we get,

6n−5n=12n=12

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