Mathematics Questions and Answers – Parallel Lines and Transversal – 4

«
»

This set of Mathematics Exam Questions and Answers for Class 9 focuses on “Parallel Lines and Transversal – 4”.

1. Find the value of k in line l || m?

a) 90°
b) 83°
c) 132°
d) 41°
View Answer

Answer: b
Explanation: line l || m

From figure, ∠1 = ∠(2x + 15)  (Vertically Opposite Angles)
∠1 + ∠(3x – 40) = 180°  (Sum of Interior Angles on the same side of transversal is 180°, l || m)
⇒ 2x + 15 + 3x – 40 = 180°
⇒ 5x = 180° + 25°
⇒ 5x = 205°
⇒ x = 41°
Now, ∠k = ∠(3x – 40) = 75°  (Alternate Interior Angles)
⇒ k = 3 x 41° – 40°
⇒ k = 83°
advertisement

2. Find the value of ∠1 and ∠2 if line p || q and ∠1 = 5x – 26°, ∠2 = 2x + 10° .

a) 90°, 90°
b) 45°, 90°
c) 41°, 41°
d) 44°, 34°
View Answer

Answer: d
Explanation:

∠1 = ∠3  (Vertically Opposite Angles)
⇒ ∠3 = 5x – 26°
Also, ∠2 = ∠3   (Corresponding Angles, p || q)
⇒ 2x + 10° = 5x – 26°
⇒ 3x = 36°
⇒ x = 12°
∠1 = 5x – 26° = 5 x 12 – 26 = 44°
and ∠2 = 2x + 10° = 2 x 12 + 10 = 34°

3. What will be the values of x and y if line AB || CD?

a) 60°, 70°
b) 75°, 75°
c) 70°, 60°
d) 60°, 120°
View Answer

Answer: a
Explanation:

Since line AB || CD , ∠(2x – y) = 60° (Vertically Opposite Angles)
⇒ 2x – y = 60°  ——- (i)
Also, ∠(x + y) + 50° = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ x + y = 130°   ——- (ii)
Adding equation (i) and (ii),
2x – y + x + y = 60° + 130°
⇒ 3x = 180°
⇒ x = 60°
Substituting value of x in equation (ii),
60° + y = 130°
⇒ y = 70°
advertisement
advertisement

4. Find the value of ∠CAB if PQ || RS and AB ⊥ RS.

a) 60°
b) 75°
c) 45°
d) 80°
View Answer

Answer: c
Explanation:

AB ⊥ RS ⇒ ∠ABC = 90°
Since line PQ || RS and AB is transversal, ∠QAB = ∠ABC = 90°   (Alternate Interior Angles)
Since line PQ || RS and AC is transversal, ∠RCA = ∠QAC = 135°   (Alternate Interior Angles)
Now, ∠CAB = ∠QAC – ∠QAB
⇒ ∠CAB = 135° – 90°
⇒ ∠CAB = 45°

5. Find the value of y if AB || CD.

a) 60°
b) 80°
c) 132°
d) 280°
View Answer

Answer: d
Explanation: Draw a line POQ parallel to AB and CD

Since line PQ || AB and OB is transversal, ∠ABO = ∠BOQ = 120°  (Alternate Interior Angles)
Since line PQ || CD and OC is transversal,
∠OCD + ∠COQ = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ ∠COQ = 180° – 140°
⇒ ∠COQ = 40°
Now, ∠BOC = ∠BOQ – ∠COQ
⇒ ∠BOC = 120° – 40°
⇒ ∠BOC = 80°
Now, y = 360° – ∠BOC   (Sum of Angles around a point is 360°)
⇒ y = 360° – 80°
⇒ y = 280°
advertisement

6. Find the value of x if BF || DE, AB ⊥ BF and ∠BAC : ∠ACB = 2 : 3.

a) 70°
b) 126°
c) 110°
d) 80°
View Answer

Answer: b
Explanation: Since AB ⊥ BF, ∠ABC = 90°
∠BAC : ∠ACB = 2 : 3
⇒ ∠BAC = 2k, ∠ACB = 3k
In ⊿ABC,
∠ABC + ∠BAC + ∠ACB = 180°  (Angle sum property of triangle)
⇒ 90° + 2k + 3k = 180°
⇒ 5k = 90°
⇒ k = 18°
∠BAC = 2 x 18 = 36°
and ∠ACB = 3 x 18 = 54°
Now, ∠ACB = ∠DCF  (Vertically Opposite Angles)
⇒ ∠DCF = 54°
Since line ED || CF and CD is transversal,
∠DCF + ∠x = 180°  (Sum of Interior Angles on the same side of transversal is 180°)
⇒ 54° + ∠x = 180°
⇒ ∠x = 126°

7. Find the value of y if PR || AC.

a) 10°
b) 25°
c) 265°
d) 120°
View Answer

Answer: c
Explanation: Draw Line XY parallel to AC and PR

Line PR || XY ⇒ ∠OQR = ∠QOX = 35°  (Alternate Interior Angles)
Line XY || AC ⇒ ∠XOA + ∠ABO = 180°  (Sum of Interior Angles on the same side of transversal)
⇒ ∠XOA + 120° = 180°
⇒ ∠XOA = 60°
Now, ∠QOX + ∠XOA + ∠QOB = 360° (Sum of Angles around a point is 360°)
⇒ 35° + 60° + y = 360°
⇒ y = 265°.
advertisement

8. Find the value of x if PQ || RS, CD || RB, ∠1 : ∠2 = 3 : 4 and ∠2 = 64°.

a) 43°
b) 54°
c) 68°
d) 72°
View Answer

Answer: b
Explanation: ∠1 : ∠2 = 3 : 4
⇒ ∠1 = 3/4 x 64°
⇒ ∠1 = 48°
Line RB || CD ⇒ ∠DCR = ∠ARB  (Corresponding Angles)
⇒ ∠DCR = 48°
Now, ∠DCP + ∠DCR + ∠RCQ = 180°  (Linear Pair)
⇒ x + 48° + 64° = 180°
⇒ x = 68°

9. Find the value of k if line l || m || n.

a) 60°
b) 54°
c) 75°
d) 120°
View Answer

Answer: a
Explanation:

From figure, ∠1 = 120°  (Vertically Opposite Angles)
Also, ∠1 + ∠2 = 180°  (Sum of Interior Angles on the same side of transversal is 180°, Line l || m )
⇒ ∠2 + 120° = 180°
⇒ ∠2 = 60°
Now, ∠k = ∠2  (Corresponding Angles, Line m || n)
⇒ k = 60°
advertisement

10. What is the value of (a + b) if Line l || m?

a) c
b) 90°
c) b + d
d) d
View Answer

Answer: c
Explanation:

From figure, ∠b = ∠d  (Corresponding Angles, Line l || m and p is transversal)
∠1 = ∠a  (Vertically Opposite Angles)
Also, ∠1 = ∠d   (Corresponding Angles, Line l || m and p is transversal)
Hence, a + b = c + d.

11. Find the value of x and y if line AB || CD.

a) 60°, 75°
b) 90°, 90°
c) 36°, 63°
d) 36°, 144°
View Answer

Answer: d
Explanation: From Figure, ∠(2x) + ∠(y) = 180°  (Linear Pair)
⇒ 2x + y = 180°  ——- (i)
Since line AB||CD, ∠( y) = ∠(3x)  (Alternate Interior Angles)
⇒ y = 3x
⇒ 3x – y = 0   ——- (ii)
Adding equation (i) and (ii),
2x + y + 3x – y = 180°
⇒ 5x = 180°
⇒ x = 36°
Substituting value of x in equation (ii),
3 x 36° – y =0
⇒ y = 144°.

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

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

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
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