Question

How many sides does a regular polygon have if each of its interior angles is

135o

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Answer 1

Answer:

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Step-by-step explanation:

The regular polygon has 8 sides. It is a regular octagon.

Step-by-step explanation:

Given,

Each interior angle of a polygon = 135°

To find, the number of sides of polygon(n) = ?

We know that,

Each interior angle of a regular convex n-gon has a measure of

\frac{(n-2)\times 180}{n}

n

(n−2)×180

\frac{(n-2)\times 180}{n}=135

n

(n−2)×180

=135

⇒ (n-2)\times 180=135n(n−2)×180=135n

⇒ 180n-360=135n180n−360=135n

⇒180n-135n=360180n−135n=360

⇒45n=36045n=360

⇒ n=\dfrac{360}{45} =8n=

45

360

=8

Hence, the regular polygon has 8 sides. It is a regular octagon