Full/Complete degree: 360°
Given degree measure of the central angle of the polygon: 6°
To find the number of sides given the central angle 6°:
360° ÷ 6° = 60 sides
The polygon has 60 sides.
Sum of interior angles of the 60-sided polygon: n (side) = 60
= (n - 2) 180°
= (60 - 2) 180°
= (58) 180°
= 10,440°
The sum of the interior angles of the 60-sided polygon is 10,440°.
Number of diagonals of the 60-sided polygon: n (side) = 60
= n (n - 3)
2
= 60 (60 -3)
2
= 60 (57)
2
= 3,420
2
= 1,710
The 60-sided polygon has 1,710 diagonals.