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Question

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

A
3 arcs
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B
6 arcs
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C
4 arcs
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D
5 arcs
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Solution

The correct option is C 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 YPA= YPB=30

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