Step-by-step explanation:
The interior angle of a polygon is given by
[tex] \frac{(n - 2) \times 180}{n} [/tex]
The exterior angle of a polygon is given by
[tex] \frac{360}{n} [/tex]
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
[tex] \frac{(n - 2) \times 180}{n} = 5( \frac{360}{n} )[/tex]
Solve the equation
That's
[tex] \frac{180n - 360}{n} = \frac{1800}{n} [/tex]
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
[tex] \frac{(12 - 2) \times 180}{12} = \frac{10 \times 180}{12} \\ = \frac{1800}{12} [/tex]
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.
