Question

The interior of a regular polygon is 5 times the exterior angle

Answer 1

Step-by-step explanation:

The interior angle of a polygon is given by

$\frac{(n - 2) \times 180}{n}$

The exterior angle of a polygon is given by

$\frac{360}{n}$

where n is the number of sides of the polygon

The statement

The interior of a regular polygon is 5 times the exterior angle is written as

$\frac{(n - 2) \times 180}{n} = 5( \frac{360}{n} )$

Solve the equation

That's

$\frac{180n - 360}{n} = \frac{1800}{n}$

Since the denominators are the same we can equate the numerators

That's

180n - 360 = 1800

180n = 1800 + 360

180n = 2160

Divide both sides by 180

n = 12

I).

The interior angle of the polygon is

$\frac{(12 - 2) \times 180}{12} = \frac{10 \times 180}{12} \\ = \frac{1800}{12}$

The answer is

150°

II.

Interior angle + exterior angle = 180

From the question

Interior angle = 150°

So the exterior angle is

Exterior angle = 180 - 150

We have the answer as

30°

III.

The polygon has 12 sides

IV.

The name of the polygon is

Dodecagon

Hope this helps you.