Question

AB, BC, and CD are the three consecutive sides of a regular polygon. If BAC = 15°;

Find:

1. Each interior angle of the polygon.
2. Each exterior angle of the polygon.
3. The number of sides of the polygon.

Answer 1

(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.