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Margaret [11]
3 years ago
12

Dina is making a logo and she decides to use a regular polygon. Each interior angle of the polygon measures 140°. What is the nu

mber of sides of this polygon?
Mathematics
1 answer:
OlgaM077 [116]3 years ago
6 0

Answer:

<em>The polygon has 9 sides (a regular nonagon).</em>

Step-by-step explanation:

<u>Angles in a Regular Polygon</u>

A polygon with n sides has a total sum of internal angles equal to 180°(n-2). This means that each angle (in a regular polygon) measures

\displaystyle \frac{180(n-2)}{n}

The regular polygon used by Dina for the logo is such that each interior angle measures 140°, thus:

\displaystyle \frac{180(n-2)}{n}=140

Multiply by n:

180(n-2)=140n

Operate:

180n-360=140n

Reducing:

40n=360

Solving:

n=9

The polygon has 9 sides (a regular nonagon).

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