Mathematics Questions and Answers – Parallel Lines and Transversal – 3

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This set of Mathematics Online Test for Class 9 focuses on “Parallel Lines and Transversal – 3”.

1. Which of the following pairs are parallel?

a) AB and CD
b) AB and PQ
c) EF and CD
d) EF and PQ
View Answer

Answer: d
Explanation: ∠AZY + ∠ZYC = 62° + 110° = 162°
Since AB and CD are two lines with PQ as transversal, ∠AZY and ∠ZYC are interior angles on the same side of transversal and their sum is not equal to 180°. So, Line AB is not parallel to CD.
Now, ∠EXY = ∠XYZ = 110°
EF and PQ are two lines with CD as transversal, ∠EXY and ∠XYZ are alternate interior angles and are equal. So, Line EF is parallel to PQ.
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2. Find the value of ∠x if line l || m and line n || p.

a) 90°
b) 75°
c) 110°
d) 120°
View Answer

Answer: b
Explanation:

∠1 = 75°  (Vertically Opposite Angles)
Line n || p ⇒ ∠1 = ∠2 = 75°  (Alternate Interior Angles)
Also, Line l || m ⇒ ∠2 = x°  (Corresponding Angles)
⇒ ∠x = 75°.

3. Find the value of k if ∠1 = 150 – k and ∠2 = 60 + k and line l || m.

a) 80°
b) 75°
c) 45°
d) 150°
View Answer

Answer: c
Explanation: Since line l || m, ∠1 = ∠2 (Corresponding Angles)
⇒ 150 – k = 60 + k
⇒ 2k = 150 – 60
⇒ k = 45°.
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4. Find the value of y if line l || m.

a) 60°
b) 75°
c) 55°
d) 80°
View Answer

Answer: a
Explanation:

∠1 + ∠(60 + y) = 180°  (Linear Pair)
⇒ ∠1 = 180° – 60° – y
⇒ ∠1 = 120° – y
Since line l || m, ∠1 = ∠y = 75°  (Alternate Interior Angles)
⇒ 120° – y = y
⇒ 2y = 120°
⇒ y = 60°.

5. Find the value of x, y and z if y : z = 2 : 3 and AB || CD.

a) 40°, 40°, 40°
b) 56°, 70°, 62°
c) 40°, 56°, 84°
d) 32°, 50°, 50°
View Answer

Answer: c
Explanation: Since line AB || CD, ∠APQ = ∠APC   (Alternate Interior Angles)
⇒ ∠x = 40°
Now, y : z = 2 : 3 ⇒ y = 2k, z = 3k  ————— (1)
Also, ∠AQR + ∠QRC = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ 40° + y + z = 180°
⇒ 40° + 2k + 3k = 180°  (From equation 1)
⇒ 5k = 140°
⇒ k = 28°
So, y = 2k = 2 x 28 = 56°
and z = 3k = 3 x 28 = 84°
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6. Find the value of ∠PQR if AB || CD || EF.

a) 70°
b) 120°
c) 110°
d) 80°
View Answer

Answer: d
Explanation: Line AB || CD || EF
Now, ∠CRS = ∠RSF = 20°   (Alternate Interior Angles, CD || EF)
Also, 120° + ∠QRC = 180°  (Sum of Interior Angles on the same side of transversal is 180°, AB || CD)
⇒ ∠QRC = 180° – 120° = 60°
Now, ∠QRS = ∠CRS + ∠QRC
⇒ ∠QRS = 20° + 60°
⇒ ∠QRS = 80°.

7. Find the value of ∠QRT if PQ || SR and SR || UT.

a) 10°
b) 20°
c) 110°
d) 120°
View Answer

Answer: a
Explanation: Extend Line SR till A

Line PQ|| RS ⇒ ∠PQR = ∠QRS = 50°  (Alternate Interior Angles)
Line PQ|| RS ⇒ ∠UTR = ∠TRA = 140°  (Alternate Interior Angles)
Also, ∠QRS + ∠QRA = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ ∠QRA = 180° – 50° = 130°
Now, ∠QRT = ∠TRA – ∠QRA
⇒ ∠QRT = 140° – 130°
⇒ ∠QRT = 10°.
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Sanfoundry Global Education & Learning Series – Mathematics – Class 9.

To practice Mathematics Online Test for Class 9, here is complete set of 1000+ Multiple Choice Questions and Answers.

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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