Question

Your aim is to construct an angle $\angle$ YPX = ${30}^{\circ }$ using a compass and a straight edge only. What is the total number of arcs (not necessarily equal in length) to be drawn to construct an angle of ${30}^{\circ }$ after drawing the base ray PX?

• A. 4 arcs
• B. 4 arcs
• C. 5 arcs
• D. 6 arcs

Answer 1

The correct option is B 4 arcs

Steps of construction:

1. Draw a ray PX.
2. With P as the centre and any radius, draw an arc, which cuts PX in A. This is the first arc.
3. With A as the centre and the same radius, cut this arc in B. This is the second arc.
4. With B as the centre and any radius more than half of AB, draw another arc as shown. This is the third arc.
5. With A as the centre and the same radius as above, cut the previously drawn arc in Y. This is the fourth arc.
6. Join P. We have our construction.