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. 4 arcs
3. 5 arcs
4. 6 arcs

Q. For constructing angle ${75}^{\circ }$
Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3: Construct _______.

(A) $\angle BAD=90°$
(B) $\angle BAD=30°$
(C) $\angle BAD=150°$
(D) $\angle BAD=45°$
[1 Mark]

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.

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. For constructing an angle of ${75}^{\circ }$

Steps of construction are:
Step 1: Draw ray AB
Step 2: Construct $\angle BAC={60}^{\circ }$
Step 3 will be

1. Bisect $\angle BAC$
2. Construct $\angle BAD={90}^{\circ }$
3. Construct $\angle BAD={60}^{\circ }$
4. Bisect $\angle CAD$

Q.

For constructing a right angle without a protractor, which of the following method/s is/are used?

1. Angle Bisector

2. ${60}^{\circ }$ angle construction

3. Median

4. Construction of triangle

Q.

For making an angle of 105${}^{\circ }$, you need to construct a 60${}^{\circ }$ angle too.

1. 

2. 

Q.

For constructing an angle of ${60}^{\circ }$, we need to draw __ arc/arcs.

Q.

Which among the following angles cannot be constructed just by using a ruler and a compass?

1. 30 degrees

2. 60 degrees

3. 70 degrees

4. 90 degrees

Q.

In the process of construction of ${45}^{\circ }$, which angle would be constructed first?

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${90}^{\circ }$
4. ${120}^{\circ }$