Construction of an Angle Bisector

Q.

How many right angles are required to create a complete angle?

1. Five

2. Two

3. Three

4. Four

Q. If we bisect the angle between ${60}^{\circ }$ and ${120}^{\circ }$, we get ___.

1. ${60}^{\circ }$
2. ${75}^{\circ }$
3. ${90}^{\circ }$
4. ${150}^{\circ }$

Q.

Which of the following is done to draw an angle of 150 degrees using compasses and a ruler?

1. 09:00

2. 06:15

3. 03:45

4. Both A & B

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

1. ${37.5}^{\circ }$
2. ${40}^{\circ }$
3. ${22.5}^{\circ }$
4. ${67.5}^{\circ }$

Q.

In the figure shown below $\angle$ABD = $\angle$DBC then ray BD is called ___ of $\angle ABC$.

1. Angle bisector

2. Perpendicular bisector

3. Median

4. None of these

Q.

Refer to the following figure:

D and C are equidistant from O.

If any point P is is located such that $△$ ODP is congurent to $△$ OCP, then P lies on the ________.

1. Perpenidicular bisector of ∠DOC

2. Angular bisector of ∠DOC

3. Altitude of ΔDOC to side DC.

4. None of these

Q. By constructing an angle bisector for each of the following angles, find out the measure of the angles that will be formed after the construction.
a) 50° b) 74° c) 105° [3 Marks]

Q. If we want to construct an angle of ${7.5}^{\circ }$, how many times should we do angular bisection and what are the angles that we should bisect? Explain.

Q.
Find the value of $\angle BAE$.

1. ${80}^{\circ }$
2. ${40}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. Observe the given construction, if $\angle BAE={60}^{\circ }$, then $\angle CAF$ will be

Q. The length of the continuous line forming the boundary of a closed geometrical figure is called its perimeter.

1. True
2. False

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.

An __ bisector is equidistant from the sides of the angle when measured along a segment perpendicular to the sides of the angle.

Q.

What is the angle that you get if you bisect an angle of ${45}^{\circ }$ ?

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

2. ${22.5}^{\circ }$

3. ${15}^{\circ }$

4. ${23.5}^{\circ }$

Q. In the following figure, if $m($arc $DXE)={100}^{\circ }$ and $m($arc $AYC)={40}^{\circ }$, find $\angle DBE$ (in ${}^{\circ }$).

Q.

A 75${}^{\circ }$ angle can be made by drawing angle bisector between a 90${}^{\circ }$ angle arm and a ___ ${}^{\circ }$arm.

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. draw a line XY .take a point a on it and construct a perpendicular AB using ruler and compasses .measure angle xab .is it a right angle?

Q.

A 75${}^{\circ }$ angle can be made by drawing angle bisector between a 90${}^{\circ }$ angle arm and a ___ angle arm.

1. 80${}^{\circ }$
2. 70${}^{\circ }$
3. 60${}^{\circ }$
4. 50${}^{\circ }$

Q.

A 75${}^{\circ }$ angle can be made by drawing angle bisector between a 90${}^{\circ }$ angle arm and a

___${}^{\circ }$ angle arm.

Q. Find the measure of the angle shown in the given figure.