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The sum of the interior angles of a certain polygon is the same as the sum of its exterior angles. How many sides does the polygon have? Select one: a. 10 b. 4 c. 8 d. 6

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kudzordzifrancis

Answer:

b. 4

Step-by-step explanation:

The sum of the interior angles of a polygon is given by the formula;

[tex](n-2)180\degree[/tex]

The sum of the exterior angles of a polygon is [tex]360\degree[/tex].

This implies that;

[tex](n-2)180\degree=360\degree[/tex]

Expand the bracket to get;

[tex]180n-360=360[/tex]

Group the like terms to get;

[tex]180n=360+360[/tex]

[tex]180n=720[/tex]

Divide by 180 to get;

[tex]n=\frac{720}{180}[/tex]

[tex]\Rightarrow n=4[/tex]

asuwafohjames

The number of sides of the polygon is 4 sides.

What is a polygon?

A polygon is a flat shape that is enclosed on all sides.

  • The sum exterior angle of a polygon = 360°
  • The sum of the interior angle of the polygon = (n-2)180

Where:

  • n = number of sides of the polygon

From the question,

  • If the sum of the interior angles = The sum of the exterior angle
  • (n-2)180 = 180............ Equation 1

Solve for n

  • (n-2) = 360/180
  • (n-2) = 2
  • n = 4 sides

Hence, The number of sides of the polygon is 4 sides.

Learn more about polygon here: https://brainly.com/question/24966296