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Question
AB, BC, and CD are the three consecutive sides of a regular polygon. If BAC = 15°;
Find:
- Each interior angle of the polygon.
- Each exterior angle of the polygon.
- The number of sides of the polygon.
Solution
(i) Let each angle of measure x degree.
Therefore, the measure of each angle will be:
x = 180° - 2 × 15° = 150°
(ii) Let each angle of measure x degree.
Therefore, the measure of each exterior angle will be :
x = 180° - 150° = 30°
(iii) Let the number of each side is n.
Now we can write
n.150° = (2n - 4) × 90°
180°n - 150°n = 360°
30°n = 360°
n = 12
Thus, the number of sides is 12.
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