Mathematics Questions and Answers – Angle Sum Property of a Quadrilateral

«
»

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Angle Sum Property of a Quadrilateral”.

1. Which of the following does not form a quadrilateral?
a)

b)

c)

d)

View Answer

Answer: b
Explanation: Sum of the four angles of the quadrilateral is always 360°. So, to check whether a given figure is quadrilateral or not, we need to check the angle sum property of the given figure.
Since the sum of angles of the figure containing angles 100°, 60°, 80°, 70° is equal to 310°, it will no form a quadrilateral.
advertisement

2. Find the value of x.

a) 105°
b) 50°
c) 60°
d) 90°
View Answer

Answer: a
Explanation: In quadrilateral ABCD,
∠A + ∠B + ∠C + ∠D = 360°  (Angle sum property of quadrilateral)
⇒ x + 100° + 80° + 75° = 360°
⇒ x = 360° – 255°
⇒ x = 105°.

3. Find the value of (x + z) if w : x : y : z = 6 : 1 : 3 : 2.

a) 30°
b) 180°
c) 120°
d) 90°
View Answer

Answer: d
Explanation: As w : x : y : z = 6 : 1 : 3 : 2, w = 6k, x = k, y = 3k and z = 2k  ——–(i)
From Figure, x + y + z + w = 360°  (Angle sum property of quadrilateral)
⇒ k + 3k + 2k + 6k = 360°  (from equation i)
⇒ 12k = 360°
⇒ k = 30°
Therefore, x + z = k + 2k = 3k = 90°.
advertisement
advertisement

4. Find the value of x and y.

a) 30°, 50°
b) 50°, 30°
c) 80°, 40°
d) 40°, 80°
View Answer

Answer: a
Explanation: From Figure, ∠PQT + ∠PQR = 180°  (Linear Pair)
⇒ 130° + 20° + x = 180°
⇒ x = 30° ———- (i)
From Figure, (x + y) + (80 + y) + (20 + x) + 100° = 360°  (Angle sum property of quadrilateral)
⇒ 200° + 2x + 2y = 360°
⇒ 60° + 2y = 160°
⇒ y = 50°.

5. What is the value of ∠BCD if BC || AD and ∠1 : ∠2 = 1 : 2?

a) 30°
b) 80°
c) 95°
d) 67°
View Answer

Answer: c
Explanation: Since BC || AD, ∠CBA + ∠DAB = 180°  (Interior angles on the same side of transversal)
⇒ 110° + 50° + ∠ABD = 180°
⇒ ∠ABD = 30°  ————- (i)
Also, ∠CBD = ∠BDA = 50°  —————– (ii) (Alternate interior angles)
Now, ∠1 : ∠2 = 1 : 2
⇒ ∠1 = ½ x 50°
⇒ ∠1 = 25°  ——————- (iii)
In quadrilateral ABCD, ∠A + ∠B + ∠C + ∠D = 360°  (Angle sum property of quadrilateral)
⇒ 110° + (50° + 30°) + (25° + 50°) + ∠C = 360°
⇒ ∠C = 95°.
advertisement

6. What is the value of ∠POQ if OP and OQ are angle bisectors?

a) 30°
b) 85°
c) 105°
d) 60°
View Answer

Answer: b
Explanation: As it is given that OP and OQ are angle bisectors, ∠SPO = ∠OPQ and ∠RQO = ∠OQP
Also, In quadrilateral PQRS, ∠P + ∠Q + ∠R + ∠S = 360°  (Angle sum property of quadrilateral)
⇒ 2∠OPQ + 2∠OQP + (110° + 60°) = 360°  (Angle bisectors)
⇒ 2(∠OPQ + ∠OQP) = 190°
⇒ (∠OPQ + ∠OQP) = 95°  ————— (i)
In ΔPOQ, ∠OPQ + ∠OQP + ∠POQ = 180°  (Angle sum property of triangle)
⇒ 95° + ∠POQ = 180°  (From equation i)
⇒ ∠POQ = 105°.

7. Which among the following relation is correct?

a) x1 + y1 > x2 + y2
b) x1 + y1 < x2 + y2
c) x1 + y1 = ½ (x2 + y2)
d) x1 + y1 = x2 + y2
View Answer

Answer: d
Explanation: From Figure,
∠QRS = 180° – y1  —————- (i) (Linear Pair)
And ∠QPS = 180° – x1  —————- (ii) (Linear Pair)
In quadrilateral PQRS, ∠P + ∠Q + ∠R + ∠S = 360°  (Angle sum property of quadrilateral)
⇒ (180° – x1) + x2 + (180° – y1) + y2 = 360°
⇒ 360° – x1 + x2 – y1 + y2 = 360°
⇒ x2 + y2 = x1 + y1.
advertisement

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

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

advertisement

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