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Question
Answer the following :
Find the number of sides of a regular polygon, if each of its interior angle is `(3pi^"c")/4`.
Solution
We know that, 1c = `(180/pi)^circ`
∴ `(3pi^"c")/4 = ((3pi)/4 xx 180/pi)^circ` = 135°
Let the number of sides of the regular polygon be n.
∴ measure of an exterior angle = `(360°)/"n"`
Since, the sum of the measures of an interior angle and an exterior angle of a polygon =180°,
`135° + (360°)/"n"` = 180°
∴ `(360°)/"n"` = 180° - 135° = 45°
∴ n = `360/45`
= 8
Hence, the number of the sides in the polygon = 8.
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