The Total Interior Angles Of A Pentagon Are 540 Degrees

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  • The total interior angles of a triangle = 180
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  • The total interior angles of a square (or rectangle) = 360
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  • The total interior angles of a pentagon = 540
  • Why must a pentagon add up to 540 (in pictures)
  • The total interior angles of a hexagon = 720
  • Why must a hexagon add up to 720 (in pictures)
  • The total interior angles of a heptagon = 900
  • Why must a heptagon add up to 900 (in pictures)
  • The total interior angles of an octagon = 1080
  • Why must an octagon add up to 1080 (in pictures)
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Feedback Privacy statement The total interior angles of a pentagon = 540°

Each time we add a side (triangle to square, square to pentagon, pentagon to hexagon) we add another 180°.

Triangle to pentagon

Triangle	Square	Pentagon
`180°`	`+`	`180°`	`+`	`180°`	`=`	`540°`

The total internal angle of a pentagon = 540°

Now divide the total internal angle by the number of corners.

i.e. divide 540° by 5.

`540^circ/5=108^circ`

1	2	3	4	5
`108°`	`+`	`108°`	`+`	`108°`	`+`	`108°`	`+`	`108°`	`=`	`540°`

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