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Each interior angle of a polygon is 135. How many sides does it have?
(a) 10
(b) 8
(c) 6
(d) 5

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Solution

(b) 8
$Interior angle = \frac{180 (n - 2)}{n} \Rightarrow 135 = \frac{180 (n - 2)}{n} \Rightarrow 135 n = 180 n - 360 \Rightarrow 360 = 180 n - 135 n \Rightarrow n = 8$

It has 8 sides.

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The exterior angle of a regular polygon is one third of its interior angle. How many sides does polygon has?

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Each interior angle of a polygon is $135^{\circ}$ . How many sides does it have?

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