Question

Your aim is to construct an angle $\angle$ YPX = ${30}^{\circ }$ using a compass and ruler only. What is the total number of arcs to be drawn to construct an angle of ${30}^{\circ }$ after drawing the base ray PX?

• A. 3 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 at point A. This is the first arc.
3. With A as the centre and with the same radius, cut the previous arc at B. This would be the second arc.
4. With B as the centre and with any radius more than half of AB, draw another arc as shown. This is the third arc.
5. With A as the centre and with the same radius as above, cut the previously drawn arc at Y. This would be the fourth arc.
6. Join PY.

In the figure shown above $\angle YPA=\angle YPB={30}^{\circ }$