Multiple choice

A regular polygen is inscribed in a circle .If a side subtend an angle of $45^{\circ}$ at the centre. What is the number of sides of the polygon?

  1. $6$
  2. $5$
  3. $10$
  4. $8$
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D Correct answer
Explanation

The central angles subtended by the sides of a regular polygon are equal and sum to 360 degrees. Therefore, the number of sides is 360/45 = 8.

AI explanation

A regular polygon inscribed in a circle divides the central 360 degree angle into equal parts. Each central angle is given as 45 degrees. We divide the full circle angle by the central angle: 360 / 45 = 8 sides.

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