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Lines and Angles MCQs for Class 9 Exam
It covers all Important Questions with answers on Lines and Angles for the Class 9 exam. The questions are based on important topics. Details about the questions:- Topic: Lines and Angles
- Type of Questions: MCQs with solutions
- Number of Questions: 23
- You can attempt them on EduRev to score high in Class 9 exam.
Two complementary angles are in the ratio 2 : 7. The measure of a smaller angle is:- a)70°
- b)45°
- c)20°
- d)40°
Correct answer is option 'C'. Can you explain this answer?
Two complementary angles are in the ratio 2 : 7. The measure of a smaller angle is:
a)
70°
b)
45°
c)
20°
d)
40°
 | Shalini Nair answered |
Let the smaller angle be 2x. Then, the larger angle is 7x.
Since the angles are complementary, we have 2x + 7x = 90.
Combining like terms, we get 9x = 90.
Dividing both sides by 9, we get x = 10.
Therefore, the smaller angle is 2x = 2(10) = 20.
So, the measure of the smaller angle is 20.
The correct answer is a) 20.
Since the angles are complementary, we have 2x + 7x = 90.
Combining like terms, we get 9x = 90.
Dividing both sides by 9, we get x = 10.
Therefore, the smaller angle is 2x = 2(10) = 20.
So, the measure of the smaller angle is 20.
The correct answer is a) 20.
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 larger angle is:- a)60°
- b)45°
- c)54°
- d)36°
Correct answer is option 'C'. Can you explain this answer?
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 larger angle is:
a)
60°
b)
45°
c)
54°
d)
36°
 | Prashansa Singh answered |
Let the measure of one angle be x. Then the measure of the other angle is 90-x.
According to the given information, 2x = 3(90-x).
Simplifying this equation, we get 2x = 270 - 3x.
Adding 3x to both sides, we get 5x = 270.
Dividing both sides by 5, we get x = 54.
Therefore, the measure of the larger angle is 90 - 54 = 36 degrees.
So, the answer is: b) 36.
According to the given information, 2x = 3(90-x).
Simplifying this equation, we get 2x = 270 - 3x.
Adding 3x to both sides, we get 5x = 270.
Dividing both sides by 5, we get x = 54.
Therefore, the measure of the larger angle is 90 - 54 = 36 degrees.
So, the answer is: b) 36.
What is the measure of an angle which is equal to 5 times its supplement?- a)150°
- b)120°
- c)90°
- d)135°
Correct answer is option 'A'. Can you explain this answer?
What is the measure of an angle which is equal to 5 times its supplement?
a)
150°
b)
120°
c)
90°
d)
135°
 | Sameer Menon answered |
The measure of an angle and its supplement add up to 180 degrees. Let's call the measure of the angle x. The measure of its supplement would then be 180 - x. According to the problem, x = 5(180 - x).
Solving this equation, we get:
x = 5(180 - x)
x = 900 - 5x
6x = 900
x = 150
Therefore, the measure of the angle is 150 degrees.
Solving this equation, we get:
x = 5(180 - x)
x = 900 - 5x
6x = 900
x = 150
Therefore, the measure of the angle is 150 degrees.
If q/p = 5, r/p = 3, then r + p =
- a)80°
- b)120°
- c)160°
- d)100°
Correct answer is option 'A'. Can you explain this answer?
If q/p = 5, r/p = 3, then r + p =
a)
80°
b)
120°
c)
160°
d)
100°
 | Shilpa Choudhury answered |
q = 5p , r = 3p and
∵ ∠POQ = 180°
⇒ p + q + r = 180°
⇒ p + 5p +3p = 180°
⇒ 9p = 180° ⇒ p = 20°
r = 3p = 3 × 20° = 60°
∴ r + p = 60° + 20° = 80°
∵ ∠POQ = 180°
⇒ p + q + r = 180°
⇒ p + 5p +3p = 180°
⇒ 9p = 180° ⇒ p = 20°
r = 3p = 3 × 20° = 60°
∴ r + p = 60° + 20° = 80°
Find x from the figure.
- a)20°
- b)25°
- c)10°
- d)15°
Correct answer is option 'A'. Can you explain this answer?
Find x from the figure.
a)
20°
b)
25°
c)
10°
d)
15°
| | Shilpa Choudhury answered |
Here ∠COQ = ∠POD [vertically opposite ∠s]
∵ ∠AOB = 180° (AOB is a straight line)
⇒ ∠POA + ∠POD + ∠BOD = 180°
⇒ 2x° +3x° + 20° +3x° = 180°
⇒ 8x = 160°
⇒ x = 20°
∵ ∠AOB = 180° (AOB is a straight line)
⇒ ∠POA + ∠POD + ∠BOD = 180°
⇒ 2x° +3x° + 20° +3x° = 180°
⇒ 8x = 160°
⇒ x = 20°
In the figure, l ∥ m, Find k.
- a)21°
- b)15°
- c)25°
- d)23°
Correct answer is option 'B'. Can you explain this answer?
In the figure, l ∥ m, Find k.
a)
21°
b)
15°
c)
25°
d)
23°
| | Shilpa Choudhury answered |
It is clear from the figure that,
105° + 5x = 180°
⇒ 5x = 75°
⇒ x = 15°
105° + 5x = 180°
⇒ 5x = 75°
⇒ x = 15°
The value of m is
- a)60°
- b)30°
- c)45°
- d)20°
Correct answer is option 'B'. Can you explain this answer?
The value of m is
a)
60°
b)
30°
c)
45°
d)
20°
| | Shilpa Choudhury answered |
∠m = ∠x [Vertically opposite ∠s]
∵ ∠AOB = 180°
⇒ ∠BOF + ∠COF + ∠AOC = 180°
⇒ ∠BOF + ∠DOE +∠AOC = 180°
⇒ x° + 2x° + 3x° = 180°
⇒ 6x° = 180°
⇒ x = 30°
∴ m = 30°
∵ ∠AOB = 180°
⇒ ∠BOF + ∠COF + ∠AOC = 180°
⇒ ∠BOF + ∠DOE +∠AOC = 180°
⇒ x° + 2x° + 3x° = 180°
⇒ 6x° = 180°
⇒ x = 30°
∴ m = 30°
The value of y, if AB || PQ is
- a)9°
- b)29°
- c)27°
- d)7°
Correct answer is option 'B'. Can you explain this answer?
The value of y, if AB || PQ is
a)
9°
b)
29°
c)
27°
d)
7°
| | Shilpa Choudhury answered |
From the figure,
(2y + y + y) + 35° = 180° (Interior ∠S)
⇒ 5y = 180° - 35°
⇒ y = 36° - 7
= 29°
(2y + y + y) + 35° = 180° (Interior ∠S)
⇒ 5y = 180° - 35°
⇒ y = 36° - 7
= 29°
AB || CD and PQ || RS, then x - y =
- a)30°
- b)60°
- c)75°
- d)90°
Correct answer is option 'C'. Can you explain this answer?
AB || CD and PQ || RS, then x - y =
a)
30°
b)
60°
c)
75°
d)
90°
| | Shilpa Choudhury answered |
∠DD1S = ∠B1D1C1 = 2x [Vertically opposite ∠S]
∠B1D1C1 + ∠A1 B1D1 = 180° [Interior ∠S]
⇒ 2x + 2y = 180°
⇒ x + y = 90° ...(i)
Also,
∠AA1C1 + ∠A1B1D1 [Corresponding ∠S]
⇒ 30° = 2y
⇒ y = 15° ...(ii)
Using (ii) in (i), we get
x = 90° - y = 90° - 15° = 75°
∠B1D1C1 + ∠A1 B1D1 = 180° [Interior ∠S]
⇒ 2x + 2y = 180°
⇒ x + y = 90° ...(i)
Also,
∠AA1C1 + ∠A1B1D1 [Corresponding ∠S]
⇒ 30° = 2y
⇒ y = 15° ...(ii)
Using (ii) in (i), we get
x = 90° - y = 90° - 15° = 75°
x = 3y = 6/7 Z, then, find the value of y.
- a)36°
- b)24°
- c)72°
- d)84°
Correct answer is option 'B'. Can you explain this answer?
x = 3y = 6/7 Z, then, find the value of y.
a)
36°
b)
24°
c)
72°
d)
84°
| | Shilpa Choudhury answered |
x = 3y, z = 21/6 y = 7/2y.
∴ x + y + z = 180°
⇒ 3y + y + 7/2 y = 180°
⇒ 4y + 7/2 y = 180°
⇒ 15y = 180° × 2
⇒ y = 24°
∴ x + y + z = 180°
⇒ 3y + y + 7/2 y = 180°
⇒ 4y + 7/2 y = 180°
⇒ 15y = 180° × 2
⇒ y = 24°
AB || CD, and ∠RQB = 115°, and ∠PRQ = 30°. The measure of ∠APC is:
- a)115°
- b)45°
- c)85°
- d)30°
Correct answer is option 'C'. Can you explain this answer?
AB || CD, and ∠RQB = 115°, and ∠PRQ = 30°. The measure of ∠APC is:
a)
115°
b)
45°
c)
85°
d)
30°
| | Shilpa Choudhury answered |
Here ∠RQB + ∠RQP =180° (∵ AB is a straight line)
⇒ ∠RQP = 180° - 115° = 65°
Now ∠PRQ = 30°
∵ ∠PRQ, ∠RQP and ∠APQ are the ∠S of D
∴ ∠PRQ + ∠RQP + ∠APQ = 180°
⇒ ∠APQ = 180°- 65°- 30° = 85°
∠APC = ∠APQ [Vertically opposite ∠S]
∴ ∠APC = 85°
⇒ ∠RQP = 180° - 115° = 65°
Now ∠PRQ = 30°
∵ ∠PRQ, ∠RQP and ∠APQ are the ∠S of D
∴ ∠PRQ + ∠RQP + ∠APQ = 180°
⇒ ∠APQ = 180°- 65°- 30° = 85°
∠APC = ∠APQ [Vertically opposite ∠S]
∴ ∠APC = 85°
If x : y = 2 : 3, then the value of y is equal to:
- a)72°
- b)36°
- c)108°
- d)144°
Correct answer is option 'C'. Can you explain this answer?
If x : y = 2 : 3, then the value of y is equal to:
a)
72°
b)
36°
c)
108°
d)
144°
| | Shilpa Choudhury answered |
∵ X : Y = 2 : 3
∴ Let the angles x and y be 2k and 3k respectively.
∴ 2k + 3k = 180°
[Sum of ∠S in the interior of transversal]
⇒ 5k = 180° ⇒ k = 36°
∴ y = 3k = 3 × 36° = 108°
∴ Let the angles x and y be 2k and 3k respectively.
∴ 2k + 3k = 180°
[Sum of ∠S in the interior of transversal]
⇒ 5k = 180° ⇒ k = 36°
∴ y = 3k = 3 × 36° = 108°
Determine the value of x from the given figure;
- a)45°
- b)22.5°
- c)25.5°
- d)25°
Correct answer is option 'B'. Can you explain this answer?
Determine the value of x from the given figure;
a)
45°
b)
22.5°
c)
25.5°
d)
25°
| | Shilpa Choudhury answered |
∠AOB = 180°
⇒ ∠AOP + ∠POB = 180°
⇒ ∠AOP + ∠POQ + ∠BOQ = 180°
⇒ 90° + 3x + x = 180°
⇒ 4x = 90°
⇒ x = 90°/4 = 22.5°
⇒ ∠AOP + ∠POB = 180°
⇒ ∠AOP + ∠POQ + ∠BOQ = 180°
⇒ 90° + 3x + x = 180°
⇒ 4x = 90°
⇒ x = 90°/4 = 22.5°
b = a + 20°, then a =
- a)145°
- b)125°
- c)130°
- d)135°
Correct answer is option 'B'. Can you explain this answer?
b = a + 20°, then a =
a)
145°
b)
125°
c)
130°
d)
135°
| | Shilpa Choudhury answered |
∵ Sum of angles around a point = 360°
∠AOB + ∠BOC = 360°
⇒ 90° + a + b = 360°
⇒ a + b = 270° ...(i) and
b = a + 20° ...(ii)
Using (ii) in (i)
a + (a + 20°) = 270°
⇒ 2a = 250°
⇒ a = 125°
∠AOB + ∠BOC = 360°
⇒ 90° + a + b = 360°
⇒ a + b = 270° ...(i) and
b = a + 20° ...(ii)
Using (ii) in (i)
a + (a + 20°) = 270°
⇒ 2a = 250°
⇒ a = 125°
In the figure, OA and OB are opposite rays ∠AOC +∠BOD = 63°. The measure of angle ∠COD is;
- a)63°
- b)127°
- c)117°
- d)27°
Correct answer is option 'C'. Can you explain this answer?
In the figure, OA and OB are opposite rays ∠AOC +∠BOD = 63°. The measure of angle ∠COD is;
a)
63°
b)
127°
c)
117°
d)
27°
| | Shilpa Choudhury answered |
∵ OA and OB are opposite rays.
∴ ∠AOB is a straight angle.
⇒ ∠AOB = 180°
⇒ (∠AOC + ∠BOD) + ∠COD = 180°
⇒ 63° + ∠COD = 180°
⇒ ∠COD = 117°
∴ ∠AOB is a straight angle.
⇒ ∠AOB = 180°
⇒ (∠AOC + ∠BOD) + ∠COD = 180°
⇒ 63° + ∠COD = 180°
⇒ ∠COD = 117°
In the adjoining figure, ∠AOQ :∠AOP = 5 : 7, then the measure of ∠BOQ is:
- a)75°
- b)105°
- c)60°
- d)120°
Correct answer is option 'B'. Can you explain this answer?
In the adjoining figure, ∠AOQ :∠AOP = 5 : 7, then the measure of ∠BOQ is:
a)
75°
b)
105°
c)
60°
d)
120°
| | Shilpa Choudhury answered |
∵ ∠POQ = 180° [PQ is a straight line]
⇒ ∠AOQ +∠AOP = 180°
⇒ 5k + 7k = 180°
⇒ 12k = 180°
⇒ k = 15°
∴ ∠BOQ = ∠AOP = 7 × 15° = 105°
[vertically opposite ∠s]
⇒ ∠AOQ +∠AOP = 180°
⇒ 5k + 7k = 180°
⇒ 12k = 180°
⇒ k = 15°
∴ ∠BOQ = ∠AOP = 7 × 15° = 105°
[vertically opposite ∠s]
POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR, then ∠POS is equal to:
- a)∠ROS - ∠QOS
- b)∠QOS - 2∠ROS
- c)∠QOS + 2∠ROS
- d)2∠ROS - ∠QOS
Correct answer is option 'B'. Can you explain this answer?
POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR, then ∠POS is equal to:
a)
∠ROS - ∠QOS
b)
∠QOS - 2∠ROS
c)
∠QOS + 2∠ROS
d)
2∠ROS - ∠QOS
| | Shilpa Choudhury answered |
Let the measure of ∠POS be x°
∵ ∠ POQ = 180°
⇒ ∠POS +∠ROS + ∠QOR = 180°
⇒ ∠POS +∠ROS + 90° = 180°
⇒ ∠ROS =(90° - x).
⇒ ∠QOS = 90° + (90° - x) = 180° - x ∴ ∠POS = x = ∠QOS - 2∠ROS.
∵ ∠ POQ = 180°
⇒ ∠POS +∠ROS + ∠QOR = 180°
⇒ ∠POS +∠ROS + 90° = 180°
⇒ ∠ROS =(90° - x).
⇒ ∠QOS = 90° + (90° - x) = 180° - x ∴ ∠POS = x = ∠QOS - 2∠ROS.
If y - x = 10°, then y =
- a) 25°
- b)20°
- c)15°
- d)10°
Correct answer is option 'A'. Can you explain this answer?
If y - x = 10°, then y =
a)
25°
b)
20°
c)
15°
d)
10°
| | Shilpa Choudhury answered |
∠AOC +∠ BOC = 180°
⇒ 7x + 3y = 180° ...(i), and
y - x = 10°
⇒ x = y -10° ...(ii)
Using (ii) and (i)
7(y - 10°) + 3y = 180°
⇒ 10y = 250°
⇒ y = 25°
⇒ 7x + 3y = 180° ...(i), and
y - x = 10°
⇒ x = y -10° ...(ii)
Using (ii) and (i)
7(y - 10°) + 3y = 180°
⇒ 10y = 250°
⇒ y = 25°
In the adjoining figure, ∠AOC + ∠BOE = 70° and ∠BOD = 40°, then measure of reflex ∠BOE is
- a)320°
- b)330°
- c)290°
- d)250°
Correct answer is option 'B'. Can you explain this answer?
In the adjoining figure, ∠AOC + ∠BOE = 70° and ∠BOD = 40°, then measure of reflex ∠BOE is
a)
320°
b)
330°
c)
290°
d)
250°
| | Shilpa Choudhury answered |
∠BOD = ∠AOC = 40°
[vertically opposite ∠s]
∵ ∠SOB is a straight angle
∴ ∠AOB = 180°
⇒ ∠AOC +∠COE +∠BOE = 180°
⇒ ∠COE = 180° - (∠AOC + ∠BOC)
= 180° - 70° = 110°
⇒ ∠AOC + ∠BOE = 70°
∠AOE = 70° - 40° = 30°
∴ reflex (∠BOC) = 360°- 30 = 330°
[vertically opposite ∠s]
∵ ∠SOB is a straight angle
∴ ∠AOB = 180°
⇒ ∠AOC +∠COE +∠BOE = 180°
⇒ ∠COE = 180° - (∠AOC + ∠BOC)
= 180° - 70° = 110°
⇒ ∠AOC + ∠BOE = 70°
∠AOE = 70° - 40° = 30°
∴ reflex (∠BOC) = 360°- 30 = 330°
Find the value of x - y + z
- a)77°
- b)85°
- c)127°
- d)137°
Correct answer is option 'A'. Can you explain this answer?
Find the value of x - y + z
a)
77°
b)
85°
c)
127°
d)
137°
| | Shilpa Choudhury answered |
∵ ∠COD = 180°
⇒ ∠BOC + ∠BOQ +∠DOQ = 180°
⇒ 55° + 60° + z = 180°
⇒ z = 65°
Similarly ∠BOC = ∠AOD
⇒ 2x + 3° = 55°
⇒ x = 26°
and,
∠AOP = ∠BOQ [vertically opposite ∠s]
⇒ 5y - 10° = 60°
⇒ y = 70°/5 = 14°
∴ x - y + z = 26° - 14° + 65° = 77°
⇒ ∠BOC + ∠BOQ +∠DOQ = 180°
⇒ 55° + 60° + z = 180°
⇒ z = 65°
Similarly ∠BOC = ∠AOD
⇒ 2x + 3° = 55°
⇒ x = 26°
and,
∠AOP = ∠BOQ [vertically opposite ∠s]
⇒ 5y - 10° = 60°
⇒ y = 70°/5 = 14°
∴ x - y + z = 26° - 14° + 65° = 77°
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