Constructing Angle Bisector

Q. Bisecting a $120$ degree angle gives degree angle.

Q.

In which of the following quadrilaterals, a diagonal is not an angle bisector?

1. Square

2. Rectangle

3. Rectangle

4. None of These

Q.

Given an angle of ${60}^{\circ }$, it is possible to get ${30}^{\circ }$.

1. True

2. False

Q.

In a straight line, what is the first basic angle that would be obtained? (in degrees)

1. ${90}^{\circ }$

2. ${270}^{\circ }$
3. ${45}^{\circ }$
4. ${180}^{\circ }$

Q.

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

1. 

2. 

Q.

Choose the correct statemet(s) about the below construction of ${60}^{\circ }$ using ruler and compass.

1. AB = AC

2. AB = BC

3. BC = AC

4. AB > AC

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
2. Construct
3. Construct
4. Bisect

Q.

Using ruler and compasses only , construct angle of measure ${45}^{\circ }$.

Q. Choose the angles among the following options which require the construction of ${60}^{\circ }$ as its first step.

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. ${120}^{\circ }$
4. all of the above

Q.

If you were given an angle of ${90}^{\circ }$, it is possible to get ${45}^{\circ }$.

1. True

2. False

Q.

Draw an angle equal to ${120}^{\circ }$. Draw the bisector of this angle.

Q.

Find the measure of the angle obtained by the bisection of angle 45°.

1. 22.5°

2. 15°

3. 35°

4. 23.5°

Q.

Refer to the following figure:

D and C are equidistant from O.

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

1. None of these

2. Perpenidicular bisector of ∠DOC

3. Altitude of ΔDOC to side DC.

4. Angular bisector of ∠DOC

Q.

To construct angle ${135}^o$ we bisect angles _____

1. 2 intersecting lines

2. 2 parallel lines

3. Both Options 1 & 2

4. Neither Option 1 nor 2

Q. In the construction of 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
2. Bisect
3. Construct
4. Construct

Q.

In the figure shown below, $\angle$ABD = $\angle$DBC, then the ray BD is called ________.

1. angle bisector

2. median
3. perpendicular bisector
4. altitude

Q.

Hari was asked to bisect a given angle, $\angle$ BOA as shown. He has done the following steps:
He draws an arc with centre O and some radius such that it cuts OB and OA at D and C respectively. Then he draws two more arcs with centres as C and D and radius more than $\frac{1}{2}$CD as shown (intersecting at Y) but has no idea why.

Select the correct statement which explains to him the reason for his construction.

Statement A : Because of equal radius, DY = CY and OD = OC. So $△$ DOY is congruent to $△$ COY

Statement B : Since OC = OD, $△$ ODC in an isosceles triangle, base angles are equal.

1. Statements A and B are true, only Statement A explains the reason.
2. Statements A and B are true, only Statement B explains the reason.
3. Statements A and B are true, but none explains the reason.
4. Statements A and B are false.

Q.

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

1. True

2. False

Q.

Given an angle of ${60}^{\circ }$, it is possible to get ${30}^{\circ }$.

1. True

2. False

Q.

In the following figure, if OQ is angle bisector of $\angle POA$, then $\angle POQ$ will be equal to ___.

1. 45°

2. 60°

3. 90°

4. 30°

Q. How many right angles are there in the letter L?

1. 1
2. 2
3. 3
4. 0

Q. A 75${}^{\circ }$ angle can be made by drawing the ___ of the angle between a ${90}^{\circ }$ angle and a ${60}^{\circ }$ angle.

Q.

In the following figure, OQ is the angle bisector of $\angle POA$
Then, what is $\angle POQ$?

1. 60°

2. 45°

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.

Draw a right angle and construct its bisector.

Q.

Refer to the following figure:
D and C are equidistant from O.
If any point P is located such that $△ODP$ is congurent to $△OCP$, then P lies on the ________.

1. angular bisector of $\angle ODP$
2. altitude of $△DOC$ to side DC
3. angle bisector of $\angle DOC$
4. None of the above

Q.

Q.

Find the measure of the angle obtained by the bisection of angle 45°.

1. 35°

2. 22.5°

3. 23.5°

4. 15°

Q.

Bisect the given angles and measure the bisected angles in the following:

∠ABC = 60°

Q.

Measure of each bisected angle of $90°$ is