Question

how many sides does a regular polygon have if each interior angle is 135°​

Answer 1

Answer:

8 sides

Step-by-step explanation:

If the interior angle is 135 degrees then the exterior angle is 180–135 = 45 degrees. This is because an exterior angle added to the interior angle must form a straight line.

The exterior angles of all regular polygons must add up to 360 degrees and therefore the number of exterior angles must be 360/45 = 8. If there are 8 exterior angles there are 8 interior angles and 8 sides.

Answer 2

Answer:

Step-by-step explanation:

Let n be the number of sides

Then sum of internal angles=(n-2)180

——-(1)

It is given that one internal angle=135

So sum of n equal internal angles=135n ————(2)

From(1) and(2)

(n-2)180=135n

180n-360=135n

180n-135n=360

45n=360

n=360/45=8

So number of sides=8