Step-by-step explanation:
The interior angle of a polygon is given by
The exterior angle of a polygon is given by
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
Solve the equation
That's
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
<h3>n = 12</h3><h2>I).</h2>The interior angle of the polygon is
The answer is
<h2>150°</h2><h2>II.</h2>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
<h2>30°</h2><h2>III.</h2>The polygon has 12 sides
<h2>IV.</h2>The name of the polygon is
<h2>Dodecagon</h2>Hope this helps you.