Answer :

Any polygon with interior angles that add up to 540 must have 5 sides and 5 corners (a pentagon). Assuming it is a regular pentagon, you need to work out what 1/5 of 540 is, which is the same as dividing it by 5. 540/5 = 108. this is the number of degrees in one interior angle of a regular pentagon.

The number of degrees in one interior angle of the polygon is 108 degrees.

What is the polygon?

A polygon is a closed two-dimensional shape having straight line segments. It is not a three-dimensional shape.

Sum of interior angles of a polygon with n sides IS;

[tex]\rm (n-2)\times 180[/tex]

Sum of interior angles of a polygon = 540°

Equating both we can determine the number of sides

[tex]\rm (n-2)\times 180=540\\\\n-2=\dfrac{540}{180}\\\\ n-2=3\\\\n=3+2\\\\n=5[/tex]

There are 5 sides in the polygon and the sum of the interior angles of a polygon is 540.

The number of degrees in one interior angle of the polygon is;

[tex]=\dfrac{540}{5}\\\\=108[/tex]

Hence, the number of degrees in one interior angle of the polygon is 108 degrees.

Learn more about interior angles here;

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