How many sides does a regular polygon have if each of its interior angles is
135o
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How many sides does a regular polygon have if each of its interior angles is
135o
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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