In the adjoining figure, $AB \| CD$ and $AB \| EF$. The value of $x$ is:
- A$50^\circ$
- B$70^\circ $
- C$40^\circ$
- ✓$60^\circ$
Answer: D.
View full solution →Question types
Lines and Angles question types
339 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
339
Questions
9
Question groups
5
Question types
01
M.C.Q
227 Q→02Assertion (A) & Reason (B) MCQ
57 Q→03True False[1 Marks ]
9 Q→04Fill In The Blanks[1 Marks ]
12 Q→051 Marks Question
3 Q→062 Marks Questions
11 Q→073 Marks Question
5 Q→085 Marks Questions
3 Q→09Case study (4 Marks)
12 Q→Sample Questions
Lines and Angles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Side $BC$ of $\triangle\text{ABC}$ has been produced to Don left-hand side and to Eon right-hand side such that $\angle\text{ABD}=125^\circ$ and$\angle\text{ACE}=130^\circ$ then $\angle\text{A}=?$
- A$55^\circ $
- B$50^\circ$
- ✓$75^\circ$
- D$65^\circ$
Answer: C.
View full solution →In figure, $\text{PQ}||\text{RS},\angle\text{QPR}=70^\circ,\angle\text{ROT}=20^\circ$ find the value of $x.$ 
- A$20^\circ$
- B$70^\circ$
- ✓$50^\circ$
- D$110^\circ$
Answer: C.
View full solution →Each angle of an equilateral triangle is:
- A$45^\circ$
- B$30^\circ$
- ✓$60^\circ$
- D$90^\circ$
Answer: C.
View full solution →The angles of a triangle are in the ratio $2 : 3 : 4$. The largest angle of the triangle is:
- A$60^\circ$
- B$100^\circ $
- C$12^\circ$
- ✓$80^\circ$
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion:
In the given figure, $AOB$ is a straight line. If
Reason: The sum of angle that are formed on a straight line is equal to $180^\circ$.
Assertion:
In the given figure, $AOB$ is a straight line. If
Reason: The sum of angle that are formed on a straight line is equal to $180^\circ$.
- ✓Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the arms form an angle of $90$ degrees between them, it is called a right angle.
Reason: Two angles whose sum is equal to $90$ degrees are called supplementary angles.
Assertion: If the arms form an angle of $90$ degrees between them, it is called a right angle.
Reason: Two angles whose sum is equal to $90$ degrees are called supplementary angles.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- ✓Assertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In the given figure, if $\text{AB}\parallel\text{CD}$ and $\angle\text{F}=30^\circ,$ then $\angle\text{FCD}$ is $120^\circ$.
Reason: If two parallel lines are intersected by a transversal, then co - interior angles are equal.
Assertion: In the given figure, if $\text{AB}\parallel\text{CD}$ and $\angle\text{F}=30^\circ,$ then $\angle\text{FCD}$ is $120^\circ$.
Reason: If two parallel lines are intersected by a transversal, then co - interior angles are equal.
- ABoth assertion and reason are true and reason is the correct explanation of assertion.
- BBoth assertion and reason are true but reason is not the correct explanation of assertion.
- ✓Assertion is true but reason is false.
- DAssertion is false but reason is true.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The name Straight - angle comes from straight - line.
Reason: The sum of angles that are formed on a straight line is equal to $180^\circ$.
Assertion: The name Straight - angle comes from straight - line.
Reason: The sum of angles that are formed on a straight line is equal to $180^\circ$.
- ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- ✓Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion:
angle $ABC = 47^\circ $.
Reason: Sum of interior opposite angles is equal to exterior angle.
Assertion:
angle $ABC = 47^\circ $.
Reason: Sum of interior opposite angles is equal to exterior angle.
- ✓Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- BBoth Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- CAssertion is true but the reason is false.
- DBoth assertion and reason are false.
Answer: A.
View full solution →The following statements are true $(T)$ and which are false $(F)?$If two adjacent angles are equal, then each angle measures 90°.
View full solution →The following statements are true $(T)$ and which are false $(F)?$ Angles forming a linear pair are supplementary.
View full solution →The following statements are true $(T)$ and which are false $(F)?$ Give reasons. Two lines perpendicular to the same line are perpendicular to each other.
View full solution →The following statements are true $(T)$ and which are false $(F)?$ Give reasons. If two lines are intersected by a transversal, then corresponding angles are equal.
View full solution →The following statements are true $(T)$ and which are false $(F)?$ Give reasons. Two lines parallel to the same line are parallel to each other.
View full solution →If two parallel lines are intersected by a transversal, then each pair of corresponding angles are ______.
If one angle of a linear pair is acute, then its other angle will be ________ .
If a transversal intersects a pair of lines in such a way that a pair of alternate angles we equal. then the lines are ______.
Two lines parallel to the same line are __________ to each other.
If the sum of two adjacent angles is $180^\circ ,$ then the _____ arms of the two angles are opposite rays.
View full solution →In the figure, $POQ$ is a line. Ray $OR$ is perpendicular to line $PQ. OS$ is another ray lying between rays $OP$ and $OR.$ Prove that $\angle ROS={1\over2}(\angle QOS-\angle POS)$
View full solution →In figure, if $x + y = w + z,$ then prove that $AOB$ is a line.
View full solution →In Fig., if $QT \perp PR, \angle TQR = 40^\circ $ and $\angle SPR = 30^\circ ,$ find $x$ and $y$
View full solution →In figure, if $P Q \| S T, \angle P Q R=110^{\circ}$ and $\angle R S T=130^{\circ}$. Find $\angle Q R S$.
View full solution →In figure, if $A B \| C D, E F \perp C D$ and $\angle G E D=126^{\circ}$. Find $\angle \mathrm{AGE}, \angle \mathrm{GEF}$ and $\angle \mathrm{FGE}$.
View full solution →In figure, if $AB \| CD, CD \| EF$ and $y : z = 3 : 7$, find $x.$
View full solution →In figure, find the values of $x$ and $y$ and then show that $AB \| CD.$
View full solution →If the $\angle X Y Z=64^{\circ}$ and $X Y$ is produced to point $P$ . Draw a figure from the given information. If ray $YQ$ bisects $\angle Z Y P$, find $\angle$ $X Y Q$ and reflex $\angle QYP$.
View full solution →In figure, $PQ$ and $RS$ are two mirrors placed parallel to each other. An incident ray $AB$ strikes the mirror $PQ$ at $B$. The reflected ray moves along the path $BC$ and strikes the mirror $RS$ at $C$ and again reflects back along $CD$. Prove that $AB \| CD.$
View full solution →In the given figure, if $AB \| CD$,$\angle$ $APQ = 50°$ and $\angle PRD = 127°$, find $x$ and $y.$
View full solution →In fig lines $XY$ and $MN$ intersect at $O$ If $\angle POY = 90$^\circ and $a:b = 2:3$ find $\angle c.$
View full solution →In fig the side $A B$ and $A C$ of $\triangle A B C$ are produced to point $E$ And $D$ respectively. If bisector $B O$ and $C O$ of $\angle C B E$ And $\angle B C D$ respectively meet at point $O$, then prove that $\angle B O C=90^{\circ}-\frac{1}{2} \angle B A C$
View full solution →In the given figure, $OP, OQ, OR$ and $OS$ are four rays. Prove that
$ \angle POQ + \angle ROQ + \angle SOR + \angle POS = 360^\circ. $
View full solution →$ \angle POQ + \angle ROQ + \angle SOR + \angle POS = 360^\circ. $
In Figure lines $AB$ and $CD$ intersect at $O$. If $\angle AOC + \angle BOE = {70^ \circ }$ and $\angle BOD = {40^ \circ }$,find $\angle BOE$ and reflex $\angle COE$
View full solution →Prove: Two distinct lines cannot have more than one point in common.
If two lines intersect, prove that the vertically opposite angles are equal.
The figure below consists of a square and an equilateral triangle connected together with a
common side.
In the design, $DF$ and $IG$ are two iron rods perpendicular to $BC.$ The measure of $\angle BAC = 120^\circ .$
$8.$ Which type of triangle is $ABC?$ Why$?$
$9.$ The central triangle AFG is equilateral. What is the measure of $\angle FDA?$
$A. 30^\circ $
$B. 60^\circ $
$C. 90^\circ $
$D. 120^\circ $
$10.$ The length of $IG$ is half of the length of $GC$. Write a proof for the statement.
View full solution →common side.
In the design, $DF$ and $IG$ are two iron rods perpendicular to $BC.$ The measure of $\angle BAC = 120^\circ .$
$8.$ Which type of triangle is $ABC?$ Why$?$
$9.$ The central triangle AFG is equilateral. What is the measure of $\angle FDA?$
$A. 30^\circ $
$B. 60^\circ $
$C. 90^\circ $
$D. 120^\circ $
$10.$ The length of $IG$ is half of the length of $GC$. Write a proof for the statement.
In the igure below, $BC = AC.$
What is the measure of $∠BAD?$
What is the measure of $∠BAD?$
- A$ 30^\circ$
- B$ 60^\circ$
- C$ 75^\circ$
- ✓$ 90^\circ$
Answer: D.
View full solution →The igure below consists of a square and an equilateral triangle connected together with a
common side.
What is the measure of $‘x’?$
common side.
What is the measure of $‘x’?$
- A$15$
- B$ 30$
- ✓$ 45$
- D$ 60$
Answer: C.
View full solution →The figure below shows an equilateral triangle bounded by two straight lines.
What is the sum of the four marked angles$?$
What is the sum of the four marked angles$?$
- A$ 180^\circ$
- ✓$ 240^\circ$
- C$ 270^\circ$
- D$ 360^\circ$
Answer: B.
View full solution →Two equilateral triangles on a straight line are shown below.What is the measure of $ 'x\ ’?$
- A$ 30$
- ✓$ 40$
- C$ 60$
- D$ 65$
Answer: B.
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