Angle Bisector

Q. In figure, $OP$ bisects $\angle BOC$ and $OQ$ bisects $\angle AOC$. Show that $\angle POQ={90}^{\circ }$

Q.

What is the measure of an angle whose bisector makes an angle of a right angle?

Q.

In the given figure, if $\angle CAD={150}^{\circ }$ and $\angle ABC={60}^{\circ },$ then reflex $\angle ACB=$___ .

1. 1 right angle

2. 2 right angles

3. 4 right angles

4. 3 right angles

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. In the given figure, OC and OE are the bisector of ∠DOB and ∠AOD respectively. Then find the measure of ∠EOC.

Q. ABCD is a kite, then which of these statements are correct?

1. Congruent triangles are formed.
2. Angle formed at point B corresponds to angle formed at point D.
3. Non congruent triangles are formed.
4. $\angle BAC=\angle DCA$

Q.

Question 1 (c)
Complete the following statement:
When we write $\angle A=\angle B$, we actually mean ___

Q. In the given figure, OB and OC are the bisectors of ∠AOD and ∠BOD respectively and ∠BOA = 30°. Then find the measure of ∠DOC.

Q. In the given figure, OC and OE are the bisector of ∠DOB and ∠AOD respectively. The measure of ∠EOC is equal to

Q. In a straight line, what is the first basic angle that would be obtained?

1. ${180}^{\circ }$
2. ${45}^{\circ }$
3. ${90}^{\circ }$
4. ${270}^{\circ }$

Q. In the given figure, O is the centre of the circle. OD is a line bisecting AB at C. Which of the following statements are true?

1. $△$AOC is congruent to $△$BOC
2. $△$AOC is not congruent to $△$BOC
3. OA = OD = OB
4. OC = OB = OA

Q. Draw an angle equal to ∠AOB, given in the adjoining figure.

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

Q.

Figure $LMNO$ maps to $L’M’N’O’$ by a ${125}^{\circ }$ rotation about point $T$

Which congruency statement is correct?

1. $\mathrm{LMNO}\cong \mathrm{L}\mathrm{M}\mathrm{N}\mathrm{O}$

2. $LMNO\cong OMNL$

3. $\mathrm{ONML}\cong \mathrm{M}\mathrm{O}\mathrm{N}\mathrm{L}$

4. $\mathrm{ONML}=\mathrm{O}\mathrm{M}\mathrm{N}\mathrm{L}$

Q. Draw four lines $OA,OB,OC,OD$ in order, $\angle AOB={48}^o$, $\angle COD={34}^o$. $OP$ bisects $\angle AOB$, $OQ$ bisects $\angle COD$. If $OQ$ is perpendicular to $OP$, calculate $\angle BOC$.

1. ${49}^o$
2. ${51}^o$
3. ${50}^o$
4. ${48}^o$

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

1. 45

Q. In the given figure, OB and OC are the bisectors of ∠AOD and ∠BOD respectively and ∠BOA = 30°. The measure of ∠DOC is equal to

Q. Look at the given shapes that are similar and find the angle which is equal to ∠DEF.

1. $\angle NMR$
2. $\angle QRM$
3. $\angle PQR$
4. $\angle OPQ$

Q. In the given figure, OB and OC are the bisectors of ∠AOD and ∠BOD respectively and ∠BOA = 30°. Then find the measure of ∠DOC.

Q. In the given figure, Tr || VS, TU || RS, $\angle RPQ$ is twice of $\angle UVS$, then find a + b

1. ${185}^{\circ }$
2. ${165}^{\circ }$
3. ${225}^{\circ }$
4. ${155}^{\circ }$

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. 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.

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. 44. Construct an angle of 127 1/2 and verify by measuring them by protactor

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.

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.

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

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.

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