Linear Pair Axiom

Q. Two angles are making a linear pair. If one of them is one third of the other, find the angles.

1. ${45}^{\circ }$
2. ${55}^{\circ }$
3. ${135}^{\circ }$
4. ${125}^{\circ }$

Q.

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

1. 

2. 

3. 

4. 

Q.

(a) Find the value of angles 2, 3, 4 if the value of angle 1 is 45. [4 MARKS]

(b) The supplementary angle of which angle is the complementary angle of ${70}^{\circ }$?

Q.

Question 12 (ii)
Find the values of the angles x, y and z in each of the following:

Q.

If$p,q,r$ are simple propositions with truth values $T,F,T$then the truth value of $\left[\right(~p\vee q)\wedge ~r]\Rightarrow p$ is

1. True

2. False

3. True, if r is false

4. None of these

Q.

(a) Find the value of angles 2, 3, 4 if $\angle$1 is 45. [4 MARKS]

(b) The supplement of which angle is the complement of ${70}^{\circ }$?

Q.

Points A, B and C are taken in such a way that they lie on the same line. Point D does not lie on the line $\overleftrightarrow{AB}$ .

Statement 1: $\angle$ABD and $\angle$DBC are supplementary

Statement 2: $\angle$ABD and $\angle$DBC form a linear pair

Choose the correct option:

1. Only Statement 2 is correct

2. Both statement 1 and 2 are correct

3. Only Statement 1 is correct

4. Neither of the statements is correct

Q.

Which of the following statements is true about the figure given below?

Given : $\angle$ABD = 110${}^{\circ }$

1. ∠DBC = 180^o

2. ∠CBA = 90^o

3. ∠CBA and ∠DBA are supplementary.

4. ∠ABD = 60^o

Q.

In the figure below, lines RS and PQ intersect each other at point O. If $\angle$POR: $\angle$ROQ = 11:13, find $\angle$SOQ.

1. $(\frac{195}{2}{)}^{\circ }$

2. ${95}^{\circ }$

3. ${65}^{\circ }$

4. $(\frac{165}{2}{)}^{\circ }$

Q. In the figure, PQ || RS, TR|| QU and $\angle PTR={42}^{\circ }$. Then $\angle QUR$ is equal to:

1. ${148}^{\circ }$
2. ${138}^{\circ }$
3. ${38}^{\circ }$
4. ${128}^{\circ }$

Q.

A ray OC is constructed on the line segment AB such that ∠BOC is x${}^{\circ }$. ∠AOC is ____

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

2. 90${}^{\circ }$ - x${}^{\circ }$

3. 360${}^{\circ }$ - x${}^{\circ }$

4. 180${}^{\circ }$ - x${}^{\circ }$

Q.

Question 97

Two angles are making a linear pair. If one of them is one-third fo the other, then find the angles.

Q.

In the figure below, x = ${30}^{\circ }$. The value of $3y$ is ___.

1. ${60}^{\circ }$
2. ${40}^{\circ }$
3. ${120}^{\circ }$
4. ${180}^{\circ }$

Q.

AOB is straight line. The value of $\angle AOP$ is ___.

1. ${70}^{\circ }$

2. ${110}^{\circ }$

3. ${120}^{\circ }$

4. ${60}^{\circ }$

Q. One angle of a linear pair is twice the other. What is the value of the smaller angle?

1. ${120}^{\circ }$
2. ${50}^{\circ }$
3. ${40}^{\circ }$
4. ${60}^{\circ }$

Q.

According to the linear pair axiom, if ray AB stands on a line PQ, then, what is the sum of the adjacent angles(in degrees)?

1. 180

2. 360

3. 90

4. 120

Q.

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

1. 

2. 

3. 

4. 

Q. Find the sum of all the angles at the five vertices of the adjoining star.

Q.

If ∠POR and ∠QOR are forming a linear pair, then find the value of x.

Q. In the given figure, if $x+y=w+z,$ then prove that $AOB$ is a line.

Q. The angles are complementary and the larger is four times the smaller.

Q. The angle which makes a linear pair with the angle measuring ${58}^{\circ }$ is :

1. ${29}^{\circ }$
2. ${61}^{\circ }$
3. ${122}^{\circ }$
4. ${199}^{\circ }$

Q.

In the figure below, lines AB and CD intersect each other at point O. Angles ($\angle$ AOD, $\angle$ COB) and ($\angle$ AOC, $\angle$ BOD) are called ___.

1. vertically opposite angles

2. opposite interior angles

3. corresponding angles

4. adjacent pair angles