Mathematics Questions and Answers – Linear Pair of Angles

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Linear Pair of Angles”.

1. Identify the linear pair of angles from the given options.

a) ∠AOB and ∠AOC
b) ∠AOC and ∠COD
c) ∠AOC and ∠COB
d) ∠AOD and ∠DOC
View Answer

Answer: c
Explanation: Two adjacent angles form a linear pair of angles if their non-common arms are two opposite rays. In the given figure, there are two linear pairs: (i) ∠AOC and ∠COB and (ii) ∠AOD and ∠DOB.
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2. Which of the following options are satisfy the condition that POQ is a line?

a) ∠POQ + ∠POR = 180°
b) ∠POR + ∠ROQ = 360°
c) ∠POR – ∠ROQ = 180°
d) ∠POR + ∠ROQ = 180°
View Answer

Answer: d
Explanation: If the sum of two adjacent angles are 180°, then their non-common arms are two opposite rays and form a linear pair of angles. In the given figure, ∠POR and ∠ROQ form a linear pair and ∠POR + ∠ROQ = 180°.

3. Find the value of k if ∠POQ and ∠POR form a linear pair.

a) 20°
b) 120°
c) 40°
d) 50°
View Answer

Answer: a
Explanation: Since ∠POQ and ∠POR form a linear pair of angles, ∠POQ + ∠POR = 180°.
From the figure, ∠POQ = 7k, ∠POR = 2k
∠POQ + ∠POR = 180°
⇒ 7k + 2k = 180°
⇒ 9k = 180°
⇒ k = 20°
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4. Find the value of ∠BOD if ∠AOD : ∠AOC = 4 : 5.

a) 20°
b) 100°
c) 140°
d) 50°
View Answer

Answer: b
Explanation: ∠AOC and ∠AOD form a linear pair of angles, ∠AOC + ∠AOD = 180°.
Also, ∠AOD: ∠AOC = 4:5
∠AOC + ∠AOD = 180°
⇒ ∠AOC + (4/5) ∠AOC = 180
⇒ 9∠AOC = 180 * 5
⇒ ∠AOC = 100°
Now, ∠BOD = ∠AOC  (Vertically opposite angles)
⇒ ∠BOD = 100°.

5. What is the value of x in the given figure?

a) 120°
b) 100°
c) 40°
d) 140°
View Answer

Answer: d
Explanation: In triangle ABC, ∠A + ∠B + ∠C = 180°
⇒ 60° + 2k + 4k = 180°
⇒ 6k = 120°
⇒ k = 20°
Now, x + ∠ABC = 180°
⇒ x + 2k = 180°
⇒ x = 180° – 2 * 20°
⇒ x = 140°
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6. Find the value of y if OF is the angle bisector of ∠COB.

a) 145°
b) 100°
c) 40°
d) 80°
View Answer

Answer: a
Explanation: Since, OF is the angle bisector of ∠COB, ∠COF = ∠BOF = 70°/2 = 35°.
∠AOC + ∠COF = 180°  (Linear Pair)
⇒ y + 35° = 180°
⇒ y = 145°

7. What is the value of ∠COF?

a) 45°
b) 150°
c) 60°
d) 180°
View Answer

Answer: c
Explanation:
∠AOC = ∠BOD = 3x  (Vertically Opposite Angles)
∠COF = ∠EOD = 4x  (Vertically Opposite Angles)
∠BOF = ∠AOE = 5x  (Vertically Opposite Angles)
Now, sum of all angles around a point is 360°
⇒ ∠BOF + ∠AOE + ∠COF + ∠EOD + ∠AOC + ∠BOD = 360°
⇒ 5x + 5x + 4x + 4x + 3x + 3x = 360°
⇒ 24x = 360°
⇒ x = 15°
∠COF = 4x = 4 x 15 = 60°
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8. What is the value of k if ∠BOD and ∠COE are right angles?

a) 30°
b) 150°
c) 60°
d) 120°
View Answer

Answer: c
Explanation: ∠BOD = ∠COE = 90°
∠BOC = 90 – k
∠EOD = 90 – k
∠BOF + ∠BOA = 180°  (Linear Pair)
⇒ (90 – k) + k + 15 + (90 – k) + 15 = 180°
⇒ k = 30°

9. Find the value of x and y if x – y = 30°.

a) 35°, 35°
b) 50°, 40°
c) 60°, 30°
d) 20°, 35°
View Answer

Answer: c
Explanation: ∠AOC + ∠BOC = 180°  (Linear Pair)
⇒ 2x + y = 180° —– (1)
Also, x – y = 30° —- (2)
Adding equation (1) and (2), we get x = 60°
Substituting the value of x in equation (1), y = 30°.
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10. Find the value of x.

a) 45°
b) 40°
c) 60°
d) 35°
View Answer

Answer: d
Explanation: ∠AOC + ∠BOC = 180°  (Linear Pair)
∠AOC = (x + 5) + x
∠BOC = (x + 10) + (x + 25)
⇒ ∠AOC + ∠BOC = 180°
⇒ (x + 5) + x + (x + 10) + (x + 25) = 180°
⇒ 4x + 40 = 180°
⇒ x = 140°/4
⇒ x = 35°

Sanfoundry Global Education & Learning Series – Mathematics – Class 9.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter