Math Question. A regular polygon has n sides. The size of each interior angle is 4 times the size of each...?

Question

A regular polygon has n sides. The size of each interior angle is 4 times the size of each exterior angle.

Calculate the size of each interior angle.
Hence, find the value of n.

Answer 1

Let the size of each exterior angle be x. Since any interior angle is supplementary to its corresponding exterior angle, we have

4x+x = 180



Solve for x,

x = 36



4x = 144 deg, the size of each interior angle.

n = 360/36 = 10 sides

Answer 2

The sum of an angle and its exterior angle always equals 180 degrees. Since the interior angle is 4 times the exterior, we can let x be the exterior and 4x equal the interior angle.



So x + 4x = 180 or 5x = 180 and x = 36 (the exterior angle)

and 4x = 144 degrees (interior angle)



also, the sum of the exterior angles is always 360 degrees



so the total of 360 divided by 36 gives 10 sides from the formula 360 / n = measure of one exterior angle.

Answer 3

180 / 5 = 36 (the exterior angle)

36 X 4 = 144 (interior angle)



the value of n is 10. but unsure on how to describe. sorry

Answer 4

a) Given: regular polygon with n sides Let 360deg/n = size of each exterior angle 8(360deg/n) = size of each interior angle. ext. angle + int. angle = 180 deg 360/n + 8(360/n) = 180 9(360/n) = 180 3240/n = 180 n = 3240/180 n = 18 ANS 360/18 = 20 deg, size of each exterior angle teddy boy

Answer 5

e = exterior

i = interior

1) e + i = 180 (exerior + interior angle must = 180)

2) 4i = e (from your question)

5i=180 (Sub 2 into 1)

i = 36



From the attached link,

360/36 =10 sides.