Two straight lines $AB$ and $CD$ cut each other at $O$. If $\angle\text{BOD}=63^\circ,$ then $\angle\text{BOC}=$
- A$63^\circ$
- ✓$117^\circ$
- C$17^\circ$
- D$153^\circ$
Answer: B.
View full solution →Question types
Lines And Angles question types
210 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
210
Questions
9
Question groups
5
Question types
01
M.C.Q
66 Q→02Assertion (A) & Reason (B) MCQ
10 Q→03True False[1 Marks ]
9 Q→04Fill In The Blanks[1 Marks ]
27 Q→051 Marks Question
20 Q→062 Marks Questions
28 Q→073 Marks Question
28 Q→08Case study (4 Marks)
1 Q→094 Marks Questions
21 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.
Given $\angle\text{POR}=3\text{x}$ and $\angle\text{QOR}=2\text{x}+10^\circ.$If $POQ$ is a straight line, then the value of $x$ is:
- A$30^\circ$
- ✓$34^\circ$
- C$36^\circ$
- DNone of these
Answer: B.
View full solution →In figure, the value of $x$, is: 
- A$12$
- B$15$
- ✓$20$
- D$30$
Answer: C.
View full solution →In figure, if lines $l$ and $m$ are parallel lines, then $x =$ 
- A$70^\circ$
- B$100^\circ $
- ✓$40^\circ$
- D$30^\circ$
Answer: C.
View full solution →In figure, if $CP || BQ$, then the measure of $x$ is: 
- ✓$130^\circ$
- B$105^\circ$
- C$175^\circ$
- D$125^\circ$
Answer: A.
View full solution →Statement-1 (A): In Fig., if $A B \| C D, \angle E A B=110^{\circ}$ and $\angle A E C=30^{\circ}$, then$\angle D C E=140^{\circ}$
Statement-2 (R): If two parallel lines are intersected by a tramsubersal, then each pair of alternate angles are equal.
Statement-2 (R): If two parallel lines are intersected by a tramsubersal, then each pair of alternate angles are equal.
- AStatement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-4
- ✓Statement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): In Fig., if $B A\|E D, B C\| E F$ and $\angle A B C=180^{\circ}$, then $\angle D E F=100^{\circ}$
Statement-2 (R): If a transbersal iniersects two parallel lines, then each pair of cornsponding angles are equal and each pair of conseculive interion angles are supplementary.
Statement-2 (R): If a transbersal iniersects two parallel lines, then each pair of cornsponding angles are equal and each pair of conseculive interion angles are supplementary.
- ✓Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-3
- BStatement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): In Fig., line lis paralld to liter m.
Statement-2 (R): If a transversal intersects two lines in such a way that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
Statement-2 (R): If a transversal intersects two lines in such a way that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
- AStatement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-2
- BStatement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- ✓Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): In fig., if $x=y$ and $a=b$, then line $I_1$ is parallel to linte $I_3$
Statement-2 (R): If a transvereral intersects two lines in such an way that a pair of corresponding angles are equal, then the two lines are parallel.
Statement-2 (R): If a transvereral intersects two lines in such an way that a pair of corresponding angles are equal, then the two lines are parallel.
- ✓Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-1
- BStatement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): In Fig. lines AB and CD intersect at O. IF $\angle A O C=40^{\circ}$, then $\angle B O C=140^{\circ}$
Statement-2 (R): If two lines intersect, then vertically opposite angles are equal.
Statement-2 (R): If two lines intersect, then vertically opposite angles are equal.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-6
- CStatement- 1 is true, Statement-2 is false.
- DStatement- 1 is false, Statement- 2 is true.
Answer: B.
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^\circ $.
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 →Fill in the blank in the following to make the statement true: If two parallel lines are intersected by a transversal, then each pair of corresponding angles are ______.
Fill in the blank so as to make the following statements true: If one angle of a linear pair is acute, then its other angle will be ________ .
Fill in the blank in the following to make the statement true: If a transversal intersects a pair of lines in such a way that a pair of alternate angles we equal. then the lines are ______.
Fill in the blank in the following to make the statement true: Two lines parallel to the same line are __________ to each other.
Fill in the blank so as to make the following statements true:If the sum of two adjacent angles is $180^\circ ,$ then the _____ arms of the two angles are opposite rays.
View full solution →Write the complement of the following angles :$ 35^\circ $
View full solution →Write the complement of the following angles: $20^\circ $
View full solution →Write the complement of the following angles:$ 30^\circ$
View full solution →Write the supplement of the following angles:$ 132^\circ $
View full solution →Write the complement of the following angles: $90^\circ$
View full solution →In figure, find the value of $x.$
View full solution →Which pair of lines in the below figure is parallel? Give reasons.
An angle is equal to $8$ times its complement. Determine its measure.
View full solution →In figure, $AOC$ is a line, find $x.$
View full solution →Write the supplement of an angle of measure $2y^\circ .$
View full solution →If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes.
Prove that the straight lines perpendicular to the same straight line are parallel to one another.
In figure, arms $BA$ and $BC$ of $\angle\text{ABC}$ are respectively parallel to arms $ED$ and $EF$ of $\angle\text{DEF}.$ Prove that $\angle\text{ABC}=\angle\text{DEF}.$
View full solution → How many pairs of adjacent angles, in all, can you name in figure $10.36$.
View full solution →In figure, $AB\ ||\ CD\ ||\ EF$ and $GH\ ||\ KL$. Find $\angle\text{HKL}.$
View full solution →'Learning by doing' has great impact in teaching of Maths. Students also enjoy Mathematics by activity method. Mr. Paul, a Mathematics teacher has explained the topic of Lines and Angles by taking a very thin steel wire. He used steel wire and made some shapes at some specific angles and shown to students and asked questions.
Choose the correct option in the following questions:
(i) What is the measure of $\angle B O D$ in figure?
(a) $90^{\circ}$$\quad$(b) $70^{\circ}$$\quad$(c) $80^{\circ}$$\quad$(d) $100^{\circ}$
(ii) What is measure of $\angle y$ in figure ?
(a) $110^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $140^{\circ}$$\quad$(d) $100^{\circ}$$\quad$
(iii) What is the measure of $\angle a$ and $\angle b$ respectively in Figure, if a : b = 2 : 3 and $O P \perp X Y$ ?
(a) $54^{\circ}, 36^{\circ}$$\quad$(b) $36^{\circ}, 54^{\circ}$$\quad$(c) $60^{\circ}, 90^{\circ}$$\quad$(d) $40^{\circ}, 60^{\circ}$
(iv) What is measure of $\angle c$ in figure ?
(a) $144^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $126^{\circ}$$\quad$(d) $120^{\circ}$
View full solution →Choose the correct option in the following questions:
(i) What is the measure of $\angle B O D$ in figure?
(a) $90^{\circ}$$\quad$(b) $70^{\circ}$$\quad$(c) $80^{\circ}$$\quad$(d) $100^{\circ}$
(ii) What is measure of $\angle y$ in figure ?
(a) $110^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $140^{\circ}$$\quad$(d) $100^{\circ}$$\quad$
(iii) What is the measure of $\angle a$ and $\angle b$ respectively in Figure, if a : b = 2 : 3 and $O P \perp X Y$ ?
(a) $54^{\circ}, 36^{\circ}$$\quad$(b) $36^{\circ}, 54^{\circ}$$\quad$(c) $60^{\circ}, 90^{\circ}$$\quad$(d) $40^{\circ}, 60^{\circ}$
(iv) What is measure of $\angle c$ in figure ?
(a) $144^{\circ}$$\quad$(b) $90^{\circ}$$\quad$(c) $126^{\circ}$$\quad$(d) $120^{\circ}$
Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.
Define complementary angles.
In figure, Line $l_1$ and $l_2$ intersect at $O$, forming angles as shown in the figure. If $x = 45$, find the value of $y, z$ and $u.$ 
View full solution →In figure, rays $OA, OB, OC, OD$ and $OE $have the common end point $O$. Show that $\angle\text{AOB}+\angle\text{BOC}+\angle\text{COD}+\angle\text{DOE}+\angle\text{EOA}=360^\circ.$ 
View full solution →In figure, lines $PQ $and $RS $intersect each other at point $O$. If $\angle\text{POR}:\angle\text{ROQ}=5:7,$ find all the angles.
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