Construction of Angles

Q.

Draw a line AB. At A, draw an arc of length $3cm$ using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure $\angle QAB$. What is the value of $\angle QAB$.

1. 120º

2. 30º

3. 90º

4. 60º

Q.

Question 84

Draw an angle of ${60}^{\circ }$ using ruler and compass and divide it into four equal parts. Measure each part.

Q.

Draw an angle of $70°$. Make a copy of it using only a straight edge and compasses.

Q.

A ${40}^{\circ }$ angle can be drawn by drawing the angle bisector of a given ${80}^{\circ }$ angle.

1. True

2. False

Q.

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

1. 

2. 

Q. Which of the following angle cannot be constructed using a compass and a ruler?

1. ${35}^{\circ }$

2. ${45}^{\circ }$

3. ${90}^{\circ }$

4. ${180}^{\circ }$

Q. Fill in the blanks to complete the steps for construction of angle.​
Steps for construction:​
A. Draw a ray QP.​
B. Draw an arc by taking as________centre with any convenient radius, which intersects QP at point N.​
C. Taking_______as the centre and the same radius as before, draw another arc which intersects the previous arc at point M.​
D. Draw QM and produce it to point R.​

∠ PQR is an angle of measure.

Q.

For the construction of an angle of measure $22{\frac{1}{2}}^{\circ }$ using a compass, which of the following angle should be constructed first?

1. 
2. 
3. 
4. 

Q.

Draw a line AB. At A, draw an arc of length $3cm$ using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure $\angle QAB$. What is the value of $\angle QAB$.

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

2. ${90}^{\circ }$

3. ${60}^{\circ }$

4. ${120}^{\circ }$

Q.

Construct with ruler and compasses ${60}^{\circ }$, ${45}^{\circ }$ and ${30}^{\circ }$ angles. [3 MARKS]

Q. Question 1
Construct an angle of ${90}^{\circ }$ at the initial point of a given ray and justify the construction.

Q.

A ray OC is constructed on the line segment AB such that ∠BOC is x${}^{\circ }$. What will be the measure of ∠AOC in terms of x?

1. x^o

2. 90^o - x^o

3. 180^o - x^o

4. 360^o - x^o

Q.

Draw a line AB. At A, draw an arc of length $3cm$ using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. Join A and P. Using the protractor, measure $\angle PAB$. What is the value of $\angle PAB$.

1. ${15}^{\circ }$

2. ${30}^{\circ }$

3. ${60}^{\circ }$

4. ${75}^{\circ }$

Q. Draw a line AB. At A, draw an arc of length $3cm$ using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure $\angle QAB$. What is the value of $\angle QAB$.

Q.

Which of the following angles can be constructed without using a protractor?

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

2. 40${}^{\circ }$

3. 50${}^{\circ }$
4. 60${}^{\circ }$

Q.

Draw a line AB. At A, draw an arc of length $3cm$ using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure $\angle QAB$. What is the value of $\angle QAB$?

1. 30º

2. 60º

3. 90º

4. 120º

Q.

Draw a line AB. At A, draw an arc of length $3cm$ using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure $\angle QAB$. What is the value of $\angle QAB$.

1. ${45}^{\circ }$

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

3. ${75}^{\circ }$

4. ${120}^{\circ }$

Q.

Question 2
Construct an angle of ${45}^{\circ }$ at the initial point of a given ray and justify the construction.

Q.

With a ruler and compass which of the following angles cannot be constructed?

1. ${80}^{\circ }$

2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. ${105}^{\circ }$

Q. Observe the given construction, AF is the angular bisector of $\angle BAE$ and AC is the angular bisector of $\angle BAF$. If $\angle BAE$ = ${60}^{\circ }$, then $\angle BAC$ will be

1. ${60}^{\circ }$
2. ${15}^{\circ }$
3. ${30}^{\circ }$
4. ${10}^{\circ }$

Q. To construct an angle of ${60}^{\circ }$

Steps of construction are:
Step 1: Draw a ray AB
Step 2 will be:

1. Taking D as center and any radius, draw an arc intersecting the previous arc at E.
2. Taking D as center and same radius, draw an arc intersecting the previous arc at E.
3. Taking A as centre and any convenient radius, draw an arc intersecting ray AB at a point D.
4. Using protractor, draw an angle ${60}^{\circ }$.

Q. Which of the following angles can be constructed with the help of simply a ruler and a pair of compass?

1. ${40}^{\circ }$
2. ${67.5}^{\circ }$
3. ${55}^{\circ }$
4. ${42.5}^{\circ }$

Q.

Which one of the following angles can not be constructed using compass and ruler?

1. ${30}^{\circ }$
2. ${15}^{\circ }$
3. ${25}^{\circ }$
4. ${45}^{\circ }$

Q.

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

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

1. Bisect $\angle CAD$

2. Bisect $\angle BAC$

3. Construct $\angle BAD={90}^{\circ }$

4. Construct $\angle BAD={60}^{\circ }$