Vertically Opposite Angles

Q. In the figure, line l ∥ line m and line p ∥ line q. Find the measures ∠ a, ∠ b, ∠ c and ∠ d.

Q.

In the given figure, which pair of angles are not supplementary?

1. $\angle 4,\angle 1$

2. $\angle 3,\angle 1$

3. $\angle 1,\angle 2$

4. $\angle 2,\angle 3$

Q. In the given figure, AB and CD are two straight lines intersecting at O. If $\angle \text{AOC and}\angle BOC\text{are 1:3 in ratio, then find}$
$\angle \text{BOD}and\angle \text{AOD, respectively}.$

1. ${135}^{\circ }\text{and}{135}^{\circ }$
2. ${45}^{\circ }\text{and}{45}^{\circ }$
3. ${135}^{\circ }\text{and}{45}^{\circ }$
4. ${45}^{\circ }\text{and}{135}^{\circ }$

Q.

In the figure below, lines RS and PQ intersect each other at point O. If $\angle POR:\angle ROQ=7:13$ , find $\angle SOQ$.

1. ${63}^{\circ }$

2. ${117}^{\circ }$

3. ${95}^{\circ }$

4. ${65}^{\circ }$

Q. Classify the following pair of angles as complementary and supplementary. [4 MARKS]

(i) ${120}^{\circ },{50}^{\circ }$

(ii) ${60}^{\circ },{120}^{\circ }$

(iii) ${39}^{\circ },{61}^{\circ }$

(iv) ${65}^{\circ },{25}^{\circ }$

Q.

In the figure given, what is the value of 't' ?

1. ${20}^{\circ }$

2. ${15}^{\circ }$

3. $5^{\circ }$

4. ${10}^{\circ }$

Q. Given below is a parallelogram $ABCD$. Complete each statement along with the definition or property used.

$\left(iv\right)$ $\angle DAB+\angle CDA=?$​

Q. At a place there is two dip circle in vertical plane perpendicular to each other. If apparent dip in them is 45 and 60 degree. The true dip angle at that place is

Q. In figure, three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of $x,y,z$ and $u$.

Q. Prove that when two lines intersect, the vertically opposite angles are equal.

Q. In the given figure, AB || CD. If ∠BAF = 120° and ∠DCE = 40°, then the value of (a + b) is

दिए गए चित्र में, AB || CD है। यदि ∠BAF = 120° तथा ∠DCE = 40°, तब (a + b) का मान है

1. 280°
2. 360°
3. 380°
4. 420°

Q.

Find angle x.

1. $x={60}^o$

2. $x={80}^o$

3. $x={120}^o$

4. $x={40}^o$

Q. When two lines intersect each other at a point, the angles opposite to each other are called _______.

1. complementary angles
2. supplementary angles
3. adjacent angles
4. vertically opposite angles

Q. In the figure below, if AB || CD, $\angle$APQ = 50${}^{\circ }$, and $\angle$PRD = 127${}^{\circ }$, find x and y.

Q.

In figure given below, find the value of $\angle$1 + $\angle$2.

1. 270${}^{\circ }$
2. 190${}^{\circ }$
3. Insufficient Data
4. 180${}^{\circ }$

Q.

Two lines PQ and LM intersect each other at a point O. Now, if the sum of ∠QOL and ∠MOP is 280^o, then ∠MOQ will be equal to

1. 75^o

2. 40^o

3. 50^o

4. 60^o

Q.

Question 66

State whether the statement is True or False.

Vertically opposite angles form a linear pair.

Q.

Select the correct option based on the given figure.

1. $\angle$u > $\angle$y

2. $\angle$u < $\angle$y

3. $\angle$u = $\angle$y

4. Insufficient data

Q.

In figure given below, find the value of $\angle$1 + $\angle$2.

1. 190${}^{\circ }$
2. 180${}^{\circ }$
3. 270${}^{\circ }$
4. Insufficient Data

Q. In the adjoining figure. line p ∥ line q. line l ∥ line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

Q.

In the given figure, if $\angle AOC$ and $\angle BOC$ are in ratio 2 : 3, find $\angle AOC$, $\angle COB$, $\angle BOD$ and $\angle AOD$.

1. ${30}^{\circ },{30}^{\circ },{120}^{\circ }and{120}^{\circ }$

2. ${50}^{\circ },{120}^{\circ },{50}^{\circ }and{120}^{\circ }$

3. ${45}^{\circ },{100}^{\circ },{45}^{\circ }and{100}^{\circ }$

4. ${72}^{\circ },{108}^{\circ },{72}^{\circ }and{108}^{\circ }$

Q. Find the value y if m || n and l is the transversal.

1. ${60}^{\circ }$
2. ${110}^{\circ }$
3. ${40}^{\circ }$
4. ${70}^{\circ }$

Q. Anmol was cutting a piece of paper with a pair of scissors. He observed that as he increases the angle of the scissors, then the vertically opposite angle ___.

1. Increases by double

2. Remains constant

3. Increases by same amount

4. Decreases by same amount

Q. In a triangle ABC, BD and CE are perpendiculars to the sides AC and AB respectively. If BD and CE intersect at I, then, $\angle BIC={180}^{\circ }-\angle A$. State true or false

1. True
2. False

Q. $\angle A$ and $\angle B$ are vertically opposite angles, and $\angle A=5x$ and $\angle B=90°+2x$. Find the value of $x$.

1. 120°
2. 90°
3. 60°
4. 30°

Q. Find x in the following figures:
(a)

(b)

Q.

Let AB and CD be two lines intersecting each other at O. If the ratio of ∠COB and ∠AOC is 5:4, then the measure of ∠AOD will be

1. 90^o

2. 80^o

3. 120^o

4. 100^o

Q. If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.

Q. Find the value y if m || n and l is the transversal.

1. ${70}^{\circ }$
2. ${40}^{\circ }$
3. ${60}^{\circ }$
4. ${110}^{\circ }$

Q. In the figure shown below, $m\angle ABD=2x,m\angle ADB=3x,m\angle APB=4xandm\angle CBQ=7x$. Therefore, $m\angle BCD$ is

1. ${90}^{\circ }$
2. ${85}^{\circ }$
3. ${72}^{\circ }$
4. ${96}^{\circ }$