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Question
The number of sides of a regular polygon whose each interior angle is of 135° is ______.
Options
6
7
8
9
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Solution
The number of sides of a regular polygon whose each interior angle is of 135° is 8.
Explanation:
We know that, the measures of each exterior angle of a polygon having n sides is given by `360^circ/n`.
∴ The number of sides,
`n = 360^circ/"Exterior angle"`
= `360^circ/(180^circ - 135^circ)` ...[∵ Exterior angle + Interior angle = 180°]
= `360^circ/45^circ`
= 8
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