Q1.
The circle has been divided into 1, 2, 3, 4, 5, 6, 8, 9, 10 and 12 parts below. What are the degree measures of the resulting angles? Write the degree measures down near the indicated angles.
Answer
A full turn is 360°. So to find each angle, simply divide 360 by the number of equal parts.
| Number of equal parts | Working | Angle of each part |
|---|---|---|
| 1 | 360 ÷ 1 | 360° |
| 2 | 360 ÷ 2 | 180° |
| 3 | 360 ÷ 3 | 120° |
| 4 | 360 ÷ 4 | 90° |
| 5 | 360 ÷ 5 | 72° |
| 6 | 360 ÷ 6 | 60° |
| 8 | 360 ÷ 8 | 45° |
| 9 | 360 ÷ 9 | 40° |
| 10 | 360 ÷ 10 | 36° |
| 12 | 360 ÷ 12 | 30° |
Why 360 was chosen: 360 can be divided exactly by every number up to 10 except 7 — and also by 12 (the months of a year) and 24 (the hours of a day). That is why each of the divisions above gives a whole number of degrees. The Rigveda too speaks of a wheel with 360 spokes.
Did you know? 360 ÷ 7 = 51.43… is not a whole number, which is exactly why the circle is never divided into 7 equal parts in this list.