Construction of an Angle Bisector

Q.

Construct an angle of ${90}^{\circ }$ using ruler and compasses and bisect it.

Q.

Construct an angle of ${22.5}^{\circ }$ without using protractor. Any of the other geometric instruments can be used. [3 MARKS]

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

1. 
2. 
3. 
4. 

Q. How many angles are formed when a transversal cuts two parallel lines?

1. 2
2. 4
3. 6
4. 8

Q.

Using protractor, draw a right angle. Bisect it to get an angle of measure ${45}^{\circ }$.

Q. What do you mean by about trisect bisect and intersect

Q.

When constructing a line parallel to a given line, you will be:

1. copying a segment

2. copying an angle

3. bisecting a segment

4. constructing a perpendicular

Q.

With the help of a ruler and a compass it is not possible to construct an angle of :

1. $37.5°$

2. $40°$

3. $22.5°$

4. $67.5°$

Q.

Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.

Q. 67.5° angle can be constructed by bisecting the angles

1. 
   30° and 90°
2. 
   60° and 90°
3. 
   45° and 90°
4. 
   45° and 60°

Q. When we bisect an angle of ${90}^{\circ }$, we get two angles.

1. $45°$
2. $30°$
3. $60°$
4. $90°$

Q. A/An is formed by two rays or two line segments that begin at the same point or share the same endpoint.

1. Line
2. Angle
3. Line segment
4. Point

Q.

Construct an angle of $90°$ at the initial point of a given ray and justify the construction.

Q. An angle bisector divides an angle into ____ equal parts.

1. two
2. three
3. four
4. None of the above

Q. Question 3 (i)
Construct the angles of the following measurements:
(i) ${30}^{\circ }$

Q.

An angle formed between east direction and north direction is

Q. In the given figure, $\angle PQR={68}^{\circ }$ and QS is the bisector of $\angle PQR,$, If QM and QN bisect $\angle PQS$ and $\angle SQR$ respectively. Then $\angle MQN,$ will be

1. 
   ${34}^{\circ }$
2. 
   ${17}^{\circ }$
3. 
   ${28}^{\circ }$
4. 
   $34{\frac{1}{2}}^{\circ }$

Q. Draw $\angle POQ$ of measure ${75}^o$ and find its line of symmetry.

Q. BF is the angle bisector of $\angle ABC$ constructed using the radius of the arc as 3 cm. If DF = 5 cm. Find the value of 2 EF + BE.

1. 10 cm
2. 13 cm
3. 5 cm
4. 20 cm

Q.

Which of the following angle can be constructed with the help of a ruler and a compass?

1. 43 degrees

2. 25 degrees

3. 22.5 degrees

4. 80 degrees

Q. Question 3
Draw an angle of ${80}^{\circ }$ with the help of protractor. Then, construct angles of
(i) ${40}^{\circ }$
(ii) ${160}^{\circ }$
(iii) ${120}^{\circ }$

Q. Is it possible to construct an angle of 75° using ruler and compass only?
(a) Yes
(b) No

Q. Construct the following angles and verify by measuring them by a protractor:
${105}^{\circ }$

[3 marks]
[NCERT]
[Construction of an Angle Bisector]

Q.

How to construct 22.5 degree ?

Q.

Create an angle of ${120}^{\circ }$ by using angle bisection while also using protractor. [2 MARKS]

Q. A 40° angle is obtained by drawing an angle bisector for a given 80° angle.

1. True
2. False
3. Cannot be determined
4. None of the above

Q.

Question 3 (iii)
Construct the angles of the following measurements:
(iii) ${15}^{\circ }$

Q.

Draw any angle with vertex $O$. Take a point $A$ on one of its arms and $B$ on another such that $OA=OB$. Draw the perpendicular bisectors of $OA$ and $OB$. Let them meet at $P$. Is $PA=PB$?

Q.

An angle of $52.5°$can be constructed. Write True or False in each of the following. Give reasons for your answer.

1. True
2. False

Q. How to draw angle 115°