Linear Pair

Q. In the given figure, $\angle AOCand\angle BOC$ form a linear pair. Determine the value of x.

1. 
2. 
3. 
4. None of these

Q. RENT is a rectangle. Its diagonals meet at O. Find 𝑥 if OR = 2𝑥 + 4 and OT = 3𝑥 + 1.

Q. In figure, ray $OS$ stands on a line $POQ$. Ray $OR$ and ray $OT$ are angle bisectors of $\angle POS$ and $\angle SOQ$, respectively. If $\angle POS=x,$ find $\angle ROT$.

Q. Find the value of x + y + z.

1. ${90}^{\circ }$
2. ${180}^{\circ }$
3. ${270}^{\circ }$
4. ${360}^{\circ }$

Q. In the given figure, PR || TV and RV ⊥ UT. If ∠PQT = 127°, ∠TRQ = 68° and x : w = 3 : 1, then which of the following options is correct?

दिए गए चित्र में, PR || TV तथा RV ⊥ UT है। यदि ∠PQT = 127°, ∠TRQ = 68° तथा x : w = 3 : 1, तब निम्नलिखित में से कौनसा विकल्प सही है?

1. x = 17°
   
2. y = 68°
   
3. y – z = 29°
   
4. x + y – z = 82°

Q. Find the values of the angles x, y and z in given figure:
[3 marks]

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

Q. In figure, $\angle AOF$ and $\angle FOG$ form a linear pair. If $\angle EOB=\angle FOC={90}^{\circ }$ and $\angle DOC=\angle FOG=\angle AOB={30}^{\circ }$
i. Name all the right angles

Q.

In the given figure, if $\frac{y}{x}=5and\frac{z}{x}=4$ , then the value of x is ${12}^{\circ }$.

1. 
2. 

Q. In the given figure AOB is a straight line. $\angle AOC=3x,\angle BOC=2x$. The value of x is

1. ${36}^{\circ }$
2. ${25}^{\circ }$
3. ${30}^{\circ }$
4. ${40}^{\circ }$

Q. $\text{In the given figure, if AB}\parallel \text{CD, l is a transversal}$
$\text{and}\angle 1={65}^{\circ },\text{then the sum of}\angle 3,\angle 5,and\angle 8$
$\text{is \_\_\_}.$

1. ${195}^{\circ }$
2. ${295}^{\circ }$
3. ${245}^{\circ }$
4. ${345}^{\circ }$

Q. Calculate the value of $x$ in the above figure.

1. ${100}^o$
2. ${120}^o$
3. ${70}^o$
4. ${125}^o$

Q. Refer to figure. Copy and complete the table :

$\angle ABD$	$\angle DBE$	$\angle EBC$
${70}^o$	${70}^o$	$?$
${50}^o$	$?$	${60}^o$
${35}^o$	${80}^o$	$?$

Q. In the figure, $\angle ABC={70}^o$ and $\angle DEF={70}^o$. Hence, with respect to the line $I$, the angles are not

1. Congruent
2. Symmetric
3. Equal
4. Identical

Q. Read the following two statements which are taken as axioms :
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to ${180}^o$.
Is this system of axioms consistent?

1. Yes
2. No
3. Ambiguous
4. Data Insufficient

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 $\left(2\angle BOE\right)$.

1. ${30}^{\circ }$

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

3. ${50}^{\circ }$

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

Q. Which of the following statements are true (T) and which are false (F) ?​

iv. If angles forming a linear pair are equal, then each of these angles is of measure ${90}^{\circ }$

Q.

Which of the following relation is true?

1. x + y + z = A + z

2. A + z = x + y

3. x + y + z = A

4. x + y + z = z

Q. Answer the following question from the figure given below:
How many pairs of interior angles on any one side of the transversal formed? Which are they?

Q. In the given figure, find $a+b$

Q. In the adjoining figure $\underset{AB}{\to }$ || $\underset{DE}{\to }$. Prove that $\angle ABC-\angle DCB+\angle CDE={180}^o$

Q.

In the figure below, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of $\angle$POS and $\angle$SOQ, respectively. If $\angle$POS = $x$, find $\angle$ROT.

1. ${90}^{\circ }$

2. ${120}^{\circ }$

3. ${75}^{\circ }$

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

Q.

In the figure, a is greater than b by one third of a right-angle. Find the values of a and b. (2 marks)

Q. In the given figure $NQ\parallel PO$. Find the value of $a$.

1. ${26}^{\circ }$
2. ${14}^{\circ }$
3. ${10}^{\circ }$
4. ${13}^{\circ }$

Q. In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x.

1. ${126}^{\circ }$
2. ${116}^{\circ }$
3. ${96}^{\circ }$
4. ${112}^{\circ }$

Q. In figure, $\angle AOF$ and $\angle FOG$ form a linear pair. If $\angle EOB=\angle FOC={90}^{\circ }$ and $\angle DOC=\angle FOG=\angle AOB={30}^{\circ }$
iii. Name three pairs of adjacent complementary angles