Respuesta :

wegnerkolmp2741o

Answer:

72 sides

Step-by-step explanation:

The sum of the angles of a polygon with n sides is (n−2) × 180

Since the polygon is regular, we can divide by the number of sides to find the measure of each angle (n−2) × 180 / n

Each angle is equal to 175

(n−2) × 180 / n = 175

Multiply each side by n

(n-2)180 = 175n

Distribute

180n -360 = 175n

Subtract 180n from each side

180n-180n-360 = 175n-180n

-360 = -5n

Divide each side by -5

-360/-5 =-5n/-5

72 = n

There are 72 sides

WeatheringWithYou

Answer: 72 sides.

Step-by-step explanation:

You can find how many sides of a regular polygon there are by using this formula:

[tex](n-2)*180 =[/tex] total angle measurement.

However, we do not have the total angle measurement. We only have one angle measure. To fix this, we can multiply it by "n", the number of sides:

[tex](n-2)*180 = tn[/tex]

Now, we have to isolate T.

[tex]\frac{180n -360}{n} = 175[/tex]

[tex]180 - \frac{360}{n} = 175[/tex]

[tex]\frac{360}{n} = 5[/tex]

n = 72.

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