A regular polygon is inscribed in a circle- If a side subtends an angle of 30- at the centre- what is the number of its sides-

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Question

A regular polygon is inscribed in a circle. If a side subtends an angle of $30^{\circ}$ at the centre, what is the number of its sides?

10

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Solution

The correct option is D $12$
For a polygon of 'n' sides, the angle subtended at the centre is $\frac{360^{o}}{n}$
Given, angle at the centre $= 30^{o}$
$=> \frac{360^{o}}{n} = 30^{o}$
$=> n = 12$
Hence, the polygon has $12$ sides.

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A regular polygon is inscribed in a circle. If a side subtends an angle of 30∘ at the centre, what is the number of its sides?

The correct option is D 12For a polygon of 'n' sides, the angle subtended at the centre is 360on Given, angle at the centre =30o=>360on=30o=>n=12 Hence, the polygon has 12 sides.

A regular polygon is inscribed in a circle. If a side subtends an angle of $30^{\circ}$ at the centre, what is the number of its sides?

The correct option is D $12$
For a polygon of 'n' sides, the angle subtended at the centre is $\frac{360^{o}}{n}$
Given, angle at the centre $= 30^{o}$
$=> \frac{360^{o}}{n} = 30^{o}$
$=> n = 12$
Hence, the polygon has $12$ sides.