Euclidea Wiki

Instruction: Construct an angle of 30° with the given side.

Goal: 3L 3E

Available tools:

  • Move
  • Point
  • Line
  • Circle
  • Perpendicular Bisector
  • Angle Bisector
  • Intersect

Pack: Beta

Previous level: 2.2

Next level: 2.4

3L 3E solution[]

2.3-3L 3E.PNG

Let A be the initial point of the given ray.

  1. Construct a circle C1 with an arbitrary center B on the ray and radius AB, intersecting the ray on C
  2. Construct the circle C2 with center C and radius BC, intersecting circle C1 on D and E
  3. Construct line AD

2V solution[]

  1. Construct line AE


You want the angle of 30° to be the inscribed angle of circle B that will subtends the same arc as a central angle of 60°, which you can get by constructing an equilateral triangle. By constructing circle C, you get BCD, an equilateral triangle, so the arc CD is the arc you want.