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taurus [48]
2 years ago
7

Find the number of sides for a regular polygon whose interior angles each measure 10 times each exterior angle

Mathematics
1 answer:
gavmur [86]2 years ago
6 0

Answer:

22 sides

Step-by-step explanation:

The expression to find an interior angle of a polygon is:

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

The expression to find an exterior angle of a polygon is:

\frac{360}{n}

Please note that "n" represents the number of sides the polygon has.

We can use these two expressions to set up an equation.

\frac{(n-2)*180}{n}=10(\frac{360}{n})

Multiply both sides by "n":

(n-2)*180=10n(\frac{360}{n})

Now, distribute:

180(n)-180(2)=\frac{3600n}{n}\\180n-360=3600

Divide both sides by 10:

\frac{180n}{10}-\frac{360}{10}=\frac{3600}{10}\\

18n-36=360

Add 36 to both sides:

18n=360+36\\18n=396

Divide both sides by 18:

n=22

The polygon has 22 sides

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