Construction of an Angle of 60 degrees

Q. 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?

1. 3 arcs
2. 5 arcs
3. 4 arcs
4. 6 arcs

Q.

Continuing with the previous question, what angle do we have at the end of four arcs?

With B as the centre and any radius more than half of AB, draw another arc as shown. This is the third arc. With A as the centre and the same radius as above, cut the previously drawn arc in Y. This would the fourth arc. Join PY.

What is ∠YPA?

1. ${30}^{\circ }$

2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${180}^{\circ }$

Q. 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?

1. 3 arcs
2. 6 arcs
3. 4 arcs
4. 5 arcs

Q.

With respect to the previous problem of construction of a ${30}^{\circ }$ angle, what angle would you get at the end of two arcs drawn in the following fashion:

With P as centre and any radius, draw an arc as shown, which cuts in A. This is the first arc. With A as centre and the same radius, cut this arc in B. This would be the second arc.

1. $\angle$ BPA = ${30}^{\circ }$

2. $\angle$ BPA = ${60}^{\circ }$
3. $\angle$ BPA = ${90}^{\circ }$
4. $\angle$ BPA = ${180}^{\circ }$

Q. Construct ${75}^{\circ }$ and verify by measuring it by a protractor. [3 MARKS]