Question

10. An exterior angle of a quadrilateral is double its immediate interior angle. What is the measure of the
exterior angle?​

Answer 1

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.

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Answer 2

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.