Question

Each interior angle of a regular polygon is double of its exterior angle. Find the
number of sides in the polygon.
of
​

Answer 1

Answer:

ANSWER

Let the number of sides in the polygon is n

Let the measure of exterior angles be x respectively.

⇒ measure of interior angle =2x

∴n×2x=(2n−4)×90°

⇒nx=(n−2)×90°.....(i)

Again, we know that,

nx=360°

(n−2)×90°=360°[From(i)]

n−2=4

⇒n=6

Hence the number of sides in the polygon are 6.

this is your answer

Answer 2

Answer:

Let the number of sides in the polygon is n

Let the measure of exterior angles be x respectively.

⇒ measure of interior angle =2x

∴n×2x=(2n−4)×90°

⇒nx=(n−2)×90°.....(i)

Again, we know that,

nx=360°

(n−2)×90°=360°[From(i)]

n−2=4

⇒n=6

Hence the number of sides in the polygon are 6.

Hope this is helpful for you.