Fundamental Concepts
15. The Degree Spin · spinning full circles into 360°
The angle measure updates dynamically as you drag point B.
A 360-degree spin is a full revolution — the arm turns in a complete circle and returns to its starting position. This angle is called a complete angle, and it divides the circle into 360 equal degrees.
What this lesson covers
Try to break it
What happens when you spin the arm all the way around? A full circle is 360°!
How you build it
Make a 120 degree angle.
- Place vertex O — the corner of the angle.
- Place point A to set the direction of the base arm.
- Draw ray OA — the base arm of the angle (Ray tool: O then A).
- With centre O, draw an arc that crosses ray OA at P. This locks the compass opening for every arc that follows.
- With centre P and the same radius, draw an arc cutting the first arc at Q. OP = PQ = OQ, so triangle OPQ is equilateral and angle POQ = 60 degrees.
- With centre Q and the same radius, draw an arc cutting the first arc at R. That is a second 60 degrees, so R lies 120 degrees from P.
- Mark point B on the crossing R — the 120 degree mark.
- Draw ray OB — the second arm. The angle AOB you have built is 120 degrees.
The proof, step by step
Prove that the angle between two adjacent hour marks on a clock is exactly 30°.
- A full rotation about the centre of a clock face measures 360°.
- The 12 hour numbers are evenly spaced, dividing that full rotation into 12 equal angles.
- When a total is split into equal parts, each part equals the total divided by the number of parts.
- Therefore, the angle between two adjacent hour marks is 360° ÷ 12 = 30°.
Worked example
A clock's minute hand makes one complete revolution every hour. Through what angle does it turn in 20 minutes?
The minute hand turns 360° in one full hour (60 minutes), so it turns 360° ÷ 60 = 6° each minute. In 20 minutes it turns 20 × 6° = 120°.
- 60°
- 90°
- 120° — correct
- 180°