Angle Bisector and It's Construction

Q. An angle bisector divides an angle into two ________ angles.

1. equal
2. right
3. congruent
4. acute

Q.

In the following diagram, measure of angle A is:

1. 120^o

2. 150^o

3. 100^o

4. 60^o

Q.

In the adjoining figure given below $ST\parallel QR$, then what is the value of y?

1. 5

2. 9

3. 12

4. 15

Q.

The sum of two adjacent angle is 110 degree . If one angle is 30 degree more than the other. Find the measures of the 2 angles.

Q.

In a quadrilateral PQRS, PQ = 3 cm, QR = 4 cm and PS = 5 cm. Also, $\angle$SPQ = ${70}^{\circ }$ and $\angle$PQR = ${90}^{\circ }$. Which of the following options is the approximate value of $\angle$QRS?

1. 

2. 

3. 

4. 

Q.

If the point on $\mathrm{y}=\mathrm{xtan}\left(\alpha \right)-\left(\frac{{\mathrm{ax}}^2}{2{\mathrm{u}}^2{\cos }^2\left(\alpha \right)}\right)(\alpha >0)$ where the tangent is parallel to $y=x$ has an ordinate $\frac{u^2}{4a}$, then $a$ is equal to

1. $\frac{\mathrm{\pi }}{6}$

2. $\frac{\mathrm{\pi }}{4}$

3. $\frac{\mathrm{\pi }}{3}$

4. $\frac{\mathrm{\pi }}{2}$

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

1. 90

Q.

How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = ${70}^{\circ }$, Angle Q = ${100}^{\circ }$, Angle R = ${80}^{\circ }$ and Angle S =${110}^{\circ }$.

1. 0

2. 1

3. 2

4. Infinite

Q. The adjacent angles are in ratio 5 : 3 and form a linear pair , find the value of the angles .

Q.

Draw an angle of measure ${153}^{°}$ and divide it into four equal parts.

Q.

Two complimentary angles are in the ratio 2:3. Find the angles

Q.

If line l is parallel to line m, then the value of x is:

1. 77^o

2. 67^o

3. 57^o

4. 87^o

Q.

It is given that $\angle$OBC is ${90}^{\circ }$.
Then, B must be the midpoint of CE.

1. True

2. False

Q. The acute angle bisector between the lines $3x-4y=0,5x+12y-26=0$ is

Q. How to construct angle AOB = 80° with compass and ruler ?

Q.

During the construction of a ${60}^{\circ }$ angle, the property of an equilateral triangle is used.

1. True

2. False

Q.

With respect to the previous problem of construction of a ${30}^{\circ }$ angle, what angle would you get at the end of two arcs drawn in the following fashion:

With P as centre and any radius, draw an arc as shown, which cuts in A. This is the first arc. With A as centre and the same radius, cut this arc in B. This would be the second arc.

1. $\angle BPA={30}^{\circ }$

2. $\angle BPA={60}^{\circ }$

3. $\angle BPA={90}^{\circ }$

4. $\angle BPA={180}^{\circ }$

Q.

The sum of two angles is 90^o and the difference between them is 10^o. Then the smaller angle is

1. 40^o

2. 64^o

3. 54^o

4. 60^o

Q.

Your aim is to construct an angle $\angle YPX={30}^{\circ }$ using a compass and a straight edge only.

What is the total number of arcs (not necessarily equal in length) to be drawn to construct an angle of ${30}^{\circ }$ after drawing the base ray PX?

1. 6 arcs

2. 4 arcs

3. 3 arcs

4. 5 arcs

Q.

In the construction of a ${90}^{\circ }$ angle, we make use of the fact that all the sides of an equilateral triangle are equal. True or False?

1. True

2. False

Q. The obtuse angle bisector between the lines $2x-y-4=0,x-2y+10=0$ is

1. $x-y+7=0$
2. $x+y-14=0$
3. $3x-y+5=0$
4. $2x+3y-5=0$

Q. Question 6
In the figure, POQ is a line. The value of x is:


A) ${20}^{\circ }$
B) ${25}^{\circ }$
C) ${30}^{\circ }$
​​​​​​​D) ${35}^{\circ }$

Q. To construct an angle of ${60}^{\circ }$

Steps of construction are:
Step1: Draw a ray AB
Step 2 will be

1. Taking D as center and any radius, draw an arc intersecting the previous arc at E
2. Taking D as center and same radius, draw an arc intersecting the previous arc at E
3. Using protractor, draw an angle
4. Taking A as centre and any convenient radius, draw an arc intersecting ray AB at a point D.

Q. In the adjoining figure, it is given that CE || BA, ∠BAC = 80° and ∠ECD = 35°.
Find (i) ∠ACE, (ii) ∠ACB, (iii) ∠ABC.

Q. The equation of the bisector of the acute angle between the lines $3x-4y+7=0$ and $12x+5y-2=0$ is

1. $11x+3y-9=0$
2. $3x-11y+9=0$
3. $11x-3y-9=0$
4. $11x-3y+9=0$

Q.

In the given figure if $\angle$ BAC = ${60}^{\circ }$, AB = AC = 6cm then find the length of BC.

1. AB=AC

2. BC = AC

3. none of the above

4. AB=BC

Q. For which of the following can a perpendicular bisector be drawn?
Line, Ray, Line segment, and Angle [1 Mark]

Q.

Is it possible to construct a unique quadrilateral ABCD with AB = 5 cm, BC = 6 cm, CD= 7 cm, $\angle$ABC = ${40}^{\circ }$ and $\angle$ BCD = ${55}^{\circ }$?

1. Yes, it is possible

2. No, two such quadrilaterals can be constructed

3. No, there can be infinite such quadrilaterals

4. With the measure of an extra side, yes.

Q.

In the adjoining figure, find the value of 'a'.

1. 60^o

2. 25^o

3. 30^o

4. 75^o

Q. Let $B_1=3x+4y-7=0\&B_2\equiv 4x-3x-14=0$ are angle bisectors of the angle between the lines $L_1=0\&L_2=0$ in which $L_1$ is passes through the point $(1,2)$ then

1. $B_1$ is acute angle bisector
2. $B_2$ is acute angle bisector
3. $B_1\&B_2$ both are right angle bisector
4. Data is insufficient