Construction of Angle Bisector of an Angle

Q.

In the given figure, $\angle$BCA = $\angle$RPQ = ${15}^{\circ }$. Find $\angle$BAC is

1. 45${}^{\circ }$
2. 15${}^{\circ }$
3. 30${}^{\circ }$
4. 60${}^{\circ }$

Q.

The Angle bisector divides an angle into two

1. equal angles

2. unequal angles

3. acute angles

4. right angles

Q. Two pipes $A$ and $B$ together can fill a cistern in $4$ hours. Had they been opened separately, then $B$ would have taken $6$ hours more than $A$ to fill the cistern. How much time will be taken by $A$ to fill the cistern separately ?

1. $1$ hours
2. $8$ hours
3. $2$ hours
4. $6$ hours

Q.

In the following figure, \(\angle\)\(POQ\) = \(\angle\)\(QOA\) = \(45^\circ\).
Then OQ is the angle bisector of \(\angle\)\(POA\).

Q. AF is the angle bisector of the angle $\angle EAD$. If AE = EF and $\angle AEF={120}^{\circ }$, the value of $\angle EAD$ is .

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${15}^{\circ }$
4. ${35}^{\circ }$

Q. The diameter of a circle is divided into n equal parts.On each part a semicircle is constructed. as n becomes very large, the sum of the lengths of the arcs of the semicircles approaches a length:

1. equal to the semi-circumference of the original circle
2. equal to the diameter of the original circle
3. greater than the semi-circumference but finite
4. that is infinite
5. greater than the diameter but less than the semi-circle

Q.

In the figure shown below $\angle$$ABD$ = ${30}^{\circ }$
BD is the angle bisector of $\angle$$ABC$. What is the value of $\angle$$ABC$.

1. ${60}^{\circ }$

2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${50}^{\circ }$

Q. Two pipes A and B can fill a cistern in $37\frac{1}{2}$ min and $45$ min respectively. Both pipes were opened and the cistern was filled in just $\frac{1}{2}$ an hour if the pipe B is turned off after what time it is opened?

1. $5$ min
2. $10$ min
3. $9$ min
4. $15$ min

Q.
MB and NB are bisectors of $\angle CBA$ and $\angle ABD$ respectively. Find the value of $\angle MBN$ (in degrees).

1. 90

Q. It is not possible to construct an angle bisector for a reflex angle.

1. True
2. False

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. The mininum number of arcs needed to construct an angle bisector is .

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

Q. Any two radii of a circle make up a diameter.

1. True
2. False