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Archy [21]
2 years ago
12

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

Mathematics
1 answer:
densk [106]2 years ago
6 0

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

<h3>n = 12</h3>

<h2>I).</h2>

The interior angle of the polygon is

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

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.

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