Question

If the measure of each interior angle of a regular polygon is 135ᵒ, then the number of sides for the polygon is

Answer 1

Answer:

135_180= 45

360/45=8

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Answer 2

Answer:

Step-by-step explanation:

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°

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

Therefore the sum of them is 135°n.

So, setting angels equal as shown below:

(n−2)×180° =135n°

⇒(n−2)×180=135n

⇒180(n−2)=135n

⇒180n−360=135n

⇒180n−135n=360

⇒45n=360

Therefor n = 8