Mathematics Questions and Answers – Parallel Lines and Transversal – 2

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Parallel Lines and Transversal – 2”.

1. Match the following pairs.

A B
i) ∠1 and ∠5 I) Interior angles
ii) ∠4 and ∠ II) Exterior Angles
iii) ∠3 and ∠5 III) Corresponding Angles
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a) i-I, ii-II, iii-III
b) i-II, ii-I, iii-III
c) i-III, ii-I, iii-II
d) i-III, ii-II, iii-I
View Answer

Answer: d
Explanation: When a transversal intersects two lines, pair of angles are formed. ∠1 and ∠5, ∠2 and ∠6, ∠4 and ∠8, ∠3 and ∠7 are corresponding angles. ∠1 and ∠7, ∠4 and ∠6 are alternate exterior angles. ∠2 and ∠8, ∠3 and ∠5 are alternate interior angles. ∠2 and ∠5, ∠3 and ∠8 are interior angles on the same side of transversal.

2. Which of the following is not correct if l || m.

a) ∠1 = ∠5
b) ∠1 = ∠3
c) ∠1 = ∠7
d) ∠2 = ∠6
View Answer

Answer: c
Explanation: When a transversal intersects two parallel lines, corresponding pair of angles are equal. ∠1 = ∠5, ∠2 = ∠6, ∠4 = ∠8, ∠3 = ∠7 as they are corresponding angles. ∠1 and ∠3 are vertically opposite angles and are equal.
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3. Find the value of x if p || q.

a) 110°
b) 360°
c) 140°
d) 80°
View Answer

Answer: a
Explanation: Line p || Line q and line t is transversal.
From figure, ∠1 = 70°  (Vertically Opposite Angles)
Also, ∠1 + x = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ x = 180° – 70°
⇒ x = 110°

4. Find the value of k if p || q.

a) 10°
b) 60°
c) 67.5°
d) 80°
View Answer

Answer: c
Explanation: Line p || Line q and line t is transversal.

From figure, ∠1 = k°  (Vertically Opposite Angles)
Also, ∠1 + (45 + k) = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ k + 45 + k = 180°
⇒ 2k = 180° – 45°
⇒ 2k = 135°
⇒ k = 67.5°
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5. Find the value of ∠5 and ∠8 if l || m and ∠1 : ∠2 = 2 : 7.

a) 10°, 70°
b) 40°, 140°
c) 110°, 70°
d) 35°, 140°
View Answer

Answer: c
Explanation: Line l || Line m and line n is transversal and ∠1 : ∠2 = 2 : 7
From figure, ∠1 + ∠2 = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ 2k + 7k = 180°
⇒ 9k = 180°
⇒ k = 20°
⇒ ∠1 = 2k = 40° and ∠2 = 7k = 140°.
Now, ∠1 = ∠5 = 40°  (Corresponding Angles)
and ∠2 = ∠8 = 140°  (Alternate Interior Angles)

6. Find the value of x if l || m || n and y : z = 5 : 4.

a) 50°
b) 60°
c) 70°
d) 80°
View Answer

Answer: d
Explanation: Line l || Line m || Line n and line t is transversal and y : z = 5 : 4

From figure, ∠1 = z  (Corresponding Angles as Line m || Line n)
∠y + ∠z = 180°   (Linear Pair)
⇒ 5k + 4k = 180°
⇒ 9k = 180°
⇒ k = 20°
⇒ ∠y = 5k = 100° and ∠z = 4k = 80°.
Now, ∠z = ∠x   (Corresponding Angles as Line l || Line m)
⇒ x = 80°.
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7. Find the value of ∠ABC if PQ|| RS.

a) 70°
b) 140°
c) 110°
d) 90°
View Answer

Answer: c
Explanation: Line PQ|| RS. Draw a line passing through B and parallel to PQ and RS

From figure, ∠1 = 50°  (Alternate Interior Angles)
Also, 120° + ∠2 = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ ∠2 = 180° – 120° = 60°
Now, ∠ABC = ∠1 + ∠2
⇒ ∠ABC = 50° + 60°
⇒ ∠ABC = 110°.

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

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Manish Bhojasia - Founder & CTO at Sanfoundry
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