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Please help with 5 and 6, show work if possible!

Please help with 5 and 6, show work if possible!-example-1
User Jumshud
by
6.8k points

1 Answer

7 votes

Answer:

6, 12

Explanation:

there are two ways to do this:

1. use the formula for the angle measure of a regular polygon: (n-2)*180 for an n-sided polygon. using this for 5 we get 120=(n-2)*180/n. multiply tboh sides by n to get 120n=(n-2)*180. expand to get 120n = 180n - 360. solve for n to get 60n = 360 so n = 6

2. using the exterior angles. the exterior angles of any polygon must add up to 360. to find the exterior angle subtract the interior angle from 180. for 6 we would do 180/150=30 so the exterior angle is 30 degrees. next, we have 30n=360 since all of the exterior angles are equal. divide both sides by 30 to get n=12

User Marc Cohen
by
6.7k points
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