Answer:
All exterior angles will add up to 360 degrees, regardless of the number of sides.
For the sum of the interior angles, use this formula:
The sum of the interior angles = (N x 180) - 360
Where N = the number of sides
So, (40 x 180) - 360 = 6840 degrees
The measure of each interior and exterior angle of a regular 40-gon are [tex]171^\circ[/tex] and [tex]9^\circ[/tex] respectively.
Important information:
Interior angle of a regular polygon is [tex]\dfrac{(n-2)\times 180^\circ}{n}[/tex], where n is the number of sides.
A regular 40-gon has 40 sides. So, the measure of each interior angle is:
[tex]\dfrac{(40-2)\times 180^\circ}{40}=38\times 4.5^\circ[/tex]
[tex]\dfrac{(40-2)\times 180^\circ}{40}=171^\circ[/tex]
Exterior angle of a regular polygon is [tex]\dfrac{360^\circ}{n}[/tex], where n is the number of sides.
A regular 40-gon has 40 sides. So, the measure of each exterior angle is:
[tex]\dfrac{360^\circ}{40}=9^\circ[/tex]
Therefore, the measure of each interior and exterior angle of a regular 40-gon are [tex]171^\circ[/tex] and [tex]9^\circ[/tex] respectively.
Find out more about 'Interior and exterior angles' here:
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