Question

how many sides does a regular polygon have if each of its exterior angle is 1350​

Answer 1

Answer:

Let the number of sides and angles of the polygon be 'n'.

The formula for the sum S of the n interior angles of an n- sided polygon is S=(n−2)×180

0

.

Since the polygon is regular, all its n interior angles are the same.

Therefore the sum of them is n×135

0

=135n

0

.

So, we also have S=135n

0

.

So, setting angels equal as shown below:

(n−2)×180

0

=135n

0

⇒(n−2)×180=135n

⇒180(n−2)=135n

⇒180n−360=135n

⇒180n−135n=360

⇒45n=360

⇒n=8

So, the regular polygon has 8 sides and is therefore, an octagon.

Step-by-step explanation:

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