Two straight lines AB and CD intersect one another at the point O. If $\angle A O C+\angle C O B+\angle B O D=274^{\circ}$, then $\angle A O D=$
- ✓$80^{\circ}$
- B$90^{\circ}$
- C$94^{\circ}$
- D$137^{\circ}$
Answer: A.
View full solution →Question types
Lines And Angles [NEW] question types
170 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
170
Questions
9
Question groups
5
Question types
01
M.C.Q
45 Q→02Assertion (A) & Reason (B) MCQ
10 Q→03Fill In The Blanks[1 Marks ]
15 Q→04True False[1 Marks ]
9 Q→051 Marks Question
12 Q→062 Marks Questions
28 Q→073 Marks Question
28 Q→084 Marks Questions
22 Q→09Case study (4 Marks)
1 Q→Sample Questions
Lines And Angles [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two straight lines AB and CD cut each other at O. If $\angle B O D=63^{\circ}$, then $\angle B O C=$
- A$63^{\circ}$
- ✓$117^{\circ}$
- C$17^{\circ}$
- D$153^{\circ}$
Answer: B.
View full solution →Two lines AB and CD intersect at O. If $\angle A O C+\angle C O B+\angle B O D=270^{\circ}$, then $\angle A O C=$
- A$70^{\circ}$
- B$80^{\circ}$
- ✓$90^{\circ}$
- D$180^{\circ}$
Answer: C.
View full solution →Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle, is
- A$45^{\circ}$
- B$30^{\circ}$
- ✓$36^{\circ}$
- Dnone of these
Answer: C.
View full solution →Two angles are supplementary. One of them is an acute angle. Which of the following could be the measure of the other angle?
- A$60^{\circ}$
- B$120^{\circ}$
- C$200^{\circ}$
- D$240^{\circ}$
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 →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. if PQ|| RS, then $\angle A C B=90^{\circ}$.
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of alternate angles are equal.
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of alternate angles are equal.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-3
- 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. if parallel lines I and m are intersected by a transversal 1, then x = 25
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of consecutive interior angles are supplementary.
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of consecutive interior angles are supplementary.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, 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 →The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is 10 deg more than the smaller, then the measures of the angles are __________.
The bisectors of two adjacent supplementary angels are always at __________.
The bisectors of a pair of vertically opposite angels are in the __________.
The angle whose supplement is three times the complement is __________.
If $x^0$ is the measure of an angle which is equal to its complement and $y^{\circ}$ is the measure of an angle which is equal to its supplement, then $\frac{x^{\circ}}{y^{\circ}}$ is equal to __________.
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°.
The following statements are true (T) and which are false (F)?
Angles forming a linear pair can both be acute angles.
The following statements are true (T) and which are false (F)?
If angles forming a linear pair are equal, then each of these angles is of measure 90°.
If angles forming a linear pair are equal, then each of these angles is of measure 90°.
The following statements are true (T) and which are false (F)?
Angles forming a linear pair are supplementary.
Angles forming a linear pair are supplementary.
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.
Two lines perpendicular to the same line are perpendicular to each other.
Write the supplement of an angle of measure $2 y^{\circ}$.
View full solution →Write the complement of an angle of measure $x^0$.
View full solution →The supplement of a right angle is __________.
The supplement of an acute angle is __________.
The complement of an acute angle is__________.
Write the supplement of an angle of measure 2y°.
Write the complement of an angle of measure x°.
Which pair of lines in the below figure is parallel? Give reasons.
Two supplementary angles differ by 48°. Find the angles.
Two supplementary angles are in the ratio 4 : 5. Find the angles.
What value of y would make AOB a line in the below figure, If $\angle\text{AOC}=4\text{y}$ and $\angle\text{BOC}=(6\text{y}+30)?$
View full solution →Two lines AB and CD intersect at O. If $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=270^\circ,$ find the measure of $\angle\text{AOC},\angle\text{COB},\angle\text{BOD}$ and $\angle\text{DOA}.$
View full solution →Prove that the straight lines perpendicular to the same straight line are parallel to one another.
In figure transversal l intersects two lines m and n, $\angle{4}=110^\circ$ and $\angle{7}=65^\circ.$ Is m || n?
View full solution →In figure, state Which lines are parallel and why.
Two unequal angles of a parallelogram are in the ratio 2 : 3. Find all its angles in degrees.
The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60°. Find the other angles.
Prove that the bisectors of a pair of vertically opposite angles are in the same straight line.
Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.
In figure, OP, OQ, OR and OS are four rays. Prove that: $\angle\text{POQ}+\angle\text{QOR}+\angle\text{SOR}+\angle\text{POS}=360^\circ$
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) $120^{\circ}$
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