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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