Vertically Opposite Angles

Q. Which direction will you face if you start facing west and makes $\frac{3}{4}$ of a revolution in the anti-clockwise direction?

Q. The vertically opposite angles are always equal.

1. True
2. False

Q. Vertically opposite angles are always:

1. Adjacent
2. Supplementary
3. Complementary
4. Equal

Q. If a and b are vertically opposite angles, then:

1. a+b=180 deg.
2. a = b
3. a+b=360 deg.
4. a+b=90 deg.

Q.

Question 10 (i)
Indicate which pairs of angles are:

Vertically opposite angles?

Q.

In the given figure, if $\angle AOB$ = 65°, then $\angle DOC$ = ____.

1. ${115}^{\circ }$

2. ${25}^{\circ }$

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

4. None

Q.

In the given figure, lines $AB$ and $CD$ intersect at $O.$ Find the value of $x+y$.

1. ${72}^{\circ }$
2. ${85}^{\circ }$
3. ${95}^{\circ }$
4. ${88}^{\circ }$

Q. If two vertically opposite angles are supplementary, then the measure of one of the angles is _________.

1. ${45}^{\circ }$
2. ${90}^{\circ }$
3. ${120}^{\circ }$
4. ${100}^{\circ }$

Q. In the given figure, $\angle COE={90}^o$. Find the value of x.

1. ${120}^{\circ }$
2. ${60}^{\circ }$
3. ${80}^{\circ }$
4. ${30}^{\circ }$

Q.

When three lines intersect at three points, then how many angles will be formed?

1. 3

2. 6

3. 12

4. 24

Q.

In the given figure, if $\angle DOB$ = 2x - 5° and $\angle AOC$ = 85°, then x = ___.

1. ${85}^{\circ }$

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

3. ${45}^{\circ }$

4. ${35}^{\circ }$

Q.

In the figure below, lines AB and CD intersect each other at point O. If the angle $\angle AOD={110}^{\circ }$ then, $\angle AOC$ is

1. ${80}^{\circ }$

2. ${100}^{\circ }$

3. ${110}^{\circ }$

4. ${70}^{\circ }$

Q. Mark the points A, B, C in the figure such that they satisfy all the three conditions.
(i) A, B in the interior of $\angle$ DOF
(ii) A, C in the exterior of $\angle$ EOF
(iii) B on $\angle$ DOE

Q. In the given figure, $AOC$ is a straight line. If angle $AOB={50}^{\circ }$, angle $AOE={90}^{\circ }$ and angle $COD={25}^{\circ }$. Find the measures of:

(iv). Reflex angle $BOD$

Q. Two lines AB and CD meet at O, $\angle DOB=(2x-5{)}^{\circ }$ and $\angle AOC={85}^{\circ }$. Find the value of $x$ in degrees.

1. 45

Q.

In the given figure, if $\angle APD$ = (3x + 15)° and $\angle CPB$ = (4x - 5)°, then x = ___.

1. ${15}^{\circ }$

2. ${20}^{\circ }$

3. ${30}^{\circ }$

4. ${25}^{\circ }$

Q.

Measure and classify each angle.

Q. In the given figure, line AC intersects BD at point O. If ∠1:∠2 = 2:3, what is the measure of ∠4?

1. ${114}^{\circ }$
2. ${78}^{\circ }$
3. ${108}^{\circ }$
4. ${118}^{\circ }$

Q.

In the figure below, lines RS and PQ intersect each other at point O. If PQ isn't perpendicular to RS, which of the following is/are true?

1. 

2. 

3. 

4. 

Q.

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

​

A. ${50}^{\circ },{67}^{\circ }$
B. ${50}^{\circ },{77}^{\circ }$
C. ${77}^{\circ },{87}^{\circ }$
D. ${77}^{\circ },{97}^{\circ }$

Q. The angle between minutes hand and hours hand at 4'O clock is congruent to________.

1. 7 O'clock
2. 8 O'clock
3. 9 O'clock
4. 12 O'clock

Q.

In the figure below, lines AB and CD intersect each other at point O. If the angle $\angle AOD={80}^{\circ }$ then, $\angle BOC$ is

1. corresponding angles

2. vertically opposite angles

3. opposite interior angles

4. adjacent pair angles

Q. In the given figure, line AB and CD intersect at O. If $\angle COB=x^{\circ }$, $\angle BOD=4x^{\circ }$ and $\angle AOD=y^{\circ }$, then y= ______ .

1. ${12}^{\circ }$
2. ${18}^{\circ }$
3. ${40}^{\circ }$
4. ${36}^{\circ }$

Q.

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

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

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

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

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

Q. In Figure , $POQ$ is a line.

Q.

(a) Find out the number of line segments in the following figure.

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


[4 MARKS]

Q.

In the given figure, line AB and CD intersect at O. If $\angle COB=x^{\circ }$, $\angle BOD=4x^{\circ }$ and $\angle AOD=y^{\circ }$, then y= ______ .

1. ${18}^{\circ }$

2. ${28}^{\circ }$

3. ${36}^{\circ }$

4. ${45}^{\circ }$

Q.

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

Q.

In the given figure, if $\angle AOC={65}^{\circ }$, then $\angle COB=$ ___.

1. ${65}^{\circ }$

2. ${105}^{\circ }$

3. ${115}^{\circ }$

4. ${80}^{\circ }$

Q.

Consider the following three statements

Statement -1: When two lines intersect each other then the linear pair of angles are always equal to the vertically opposite angles.
Statement-2: If a ray stands on a line, then the sum of two adjacent angles so formed is ${180}^{\circ }$
Statement -3: In a right angle triangle between the other two angles one is obtuse and the other is acute.
Which of the following is correct.

1. Statements 1 and 2 are true and statement 3 is false.

2. All the Statements are true.

3. Statements 1 and 3 are false and statement 2 is true.

4. Statements 2 and 3 are true and statement 1 is false.