Angle Bisector

Q.

After angle bisection, the obtained angle is 52 degrees. What is the measure of the angle that was bisected?

1. 104 degrees

2. 94 degrees

3. 112 degrees

4. 100 degrees

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.

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

Q.

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

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

Q. Draw an angle of 75° and draw its bisector.
[3 marks]

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 in D and C. Then he marks two more arcs with centres as C and D and radius more than $\frac{1}{2}CD$ as shown (intersecting in Y) but has no idea why.

Select the correct statement which explains him the reason.

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

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 in D and C. Then he marks two more arcs with centres as C and D and radius more than $\frac{1}{2}CD$ as shown (intersecting in Y) but has no idea why.

Select the correct statement which explains him the reason.

Statement A : Because of equal radius, DY = CY and OD = OC. So $△$ DOY is congurent 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. In which of the following situations an angle bisector cannot be constructed to bisect the angle formed between two given lines?

1. Two intersecting lines
2. Two parallel lines
3. Two perpendicular lines
4. None of the above

Q.

The measure of the angle obtained when angle bisector construction is used to bisect an angle of 342 degrees is

1. 171 degrees

2. 287 degrees

3. 152 degrees

4. 300 degrees