Linear Pair and Its Axioms

Q.

Which one of the following statements are true?

1. If two angles form a linear pair, then each of these angles is of measure ${180}^{\circ }$.

2. Angles forming a linear pair can both be acute angles.

3. One of the angles forming a linear pair can be obtuse angle.

4. The sum of the angles of a linear pair is ${180}^{\circ }$.

Q.

In the given figure AB and CD are two lines intersecting at O. If $\angle AOC$ and $\angle BOC$ are in ratio 2 : 3, find all angles.

1. ${72}^{\circ },{108}^{\circ },{108}^{\circ },{72}^{\circ }$
2. ${30}^{\circ },{120}^{\circ },{30}^{\circ },{120}^{\circ }$
3. ${50}^{\circ },{120}^{\circ },{50}^{\circ },{120}^{\circ }$
4. ${45}^{\circ },{100}^{\circ },{100}^{\circ },{45}^{\circ }$

Q.

If one angle of a linear pair is obtuse angle, what kind of angle is the other?

Q.

From the adjoining figure, if $\angle$2 = 55${}^{\circ }$ and $\angle$5 = 60${}^{\circ }$ then the lines m and n are

​

1. Parallel

2. Not parallel

3. Intersect at two points

4. Concurrent

Q. Given that lines m and n are parallel, find the measure of $\angle 1$.

1. 121°
2. 153°
3. 105°
4. 144°

Q. In the given figure, if the measure of the angles x, y and z are in the ratio 2 : 3 : 4, then find the measure of angle x.

1. 40°
2. 60°
3. 80°
4. 75°

Q.

In the figure below, lines AB and CD intersect at O. If $\angle$AOC + $\angle$BOE = ${70}^{\circ }$ and $\angle$BOD = ${40}^{\circ }$, find (2$\angle$BOE).

1. 

2. 

3. 

4. 

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. Line DE intersects PQ at O. If $\angle POE=3Y,\angle QOE=2X$ and X = ${30}^{\circ }$, then (6Y - 3X)=

1. ${60}^{\circ }$
2. ${150}^{\circ }$
3. ${180}^{\circ }$

Q.

In the figure given, if AB || CD, Find the values of 'p' and 'q'.

Q. Question 2
In the given figure, lines XY and MN intersect at O. If $\angle POY={90}^{\circ }$ and a:b = 2:3, find c.

Q.

In the given figure, AB and CD are two lines intersecting at O. If $\angle AOC$ and $\angle BOC$ are in ratio 2 : 3, find all angles.

1. ${45}^{\circ },{100}^{\circ },{100}^{\circ },{45}^{\circ }$
2. ${30}^{\circ },{120}^{\circ },{30}^{\circ },{120}^{\circ }$
3. ${72}^{\circ },{108}^{\circ },{108}^{\circ },{72}^{\circ }$
4. ${50}^{\circ },{120}^{\circ },{50}^{\circ },{120}^{\circ }$

Q.

In the figure below, lines AB and CD intersect at O. If $\angle$AOC + $\angle$BOE = ${70}^{\circ }$ and $\angle$BOD = ${40}^{\circ }$,
find (2$\angle$BOE).

1. 

2. 

3. 

4. 

Q.

In the given figure AB and CD are two lines intersecting at O. If $\angle AOC$ and $\angle BOC$ are in ratio 2 : 3, find all angles.

1. ${72}^{\circ },{108}^{\circ },{108}^{\circ },{72}^{\circ }$
2. ${45}^{\circ },{100}^{\circ },{100}^{\circ },{45}^{\circ }$
3. ${30}^{\circ },{120}^{\circ },{30}^{\circ },{120}^{\circ }$
4. ${50}^{\circ },{120}^{\circ },{50}^{\circ },{120}^{\circ }$

Q. In the given figure, $\overline{AB}$ is a straight line. Find the
value of $x$. Also find $\angle AOC,\angle COD$ and $\angle BOD$.

Q. Measure of one angle of linear pair is given. Find the measure of another angle:
${50}^{\circ }$.

Q. If angle S and 100° forms a linear pair, what is the value of angle S?

1. 70°
2. 100°
3. 90°
4. 80°

Q. When adjacent angles are supplementary then they are called linear pair.

1. True
2. False

Q.

In the figure below, lines XY and MN intersect at point O. If $\angle$POY = ${90}^{\circ }$ and $\angle$ A : $\angle$ B = 2 : 3, find $\frac{\left(\angle C\right)}{2}$.

1. ${77.5}^{\circ }$
2. ${63}^{\circ }$
3. ${55}^{\circ }$
4. ${68}^{\circ }$

Q. Lines AB and CD intersect at point O. If $\angle AOD={50}^{\circ }$, then match the following.

1. ${50}^{\circ }$
2. ${130}^{\circ }$
3. ${40}^{\circ }$
4. ${310}^{\circ }$

Q.

In the figure below, lines AB and CD intersect at O. If $\angle$AOC + $\angle$BOE = ${70}^{\circ }$ and $\angle$BOD = ${40}^{\circ }$, find (2 $\angle$BOE).

1. ${50}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. In the given figure, lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ intersect at O. If $\angle AOC+\angle BOE={70}^o$ and $\angle BOD={40}^o$, find $\angle BOE$ and reflex $\angle COE$.