Mathematics Questions and Answers – Visualising Solid Shapes – Faces Edges and Vertices

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Visualising Solid Shapes – Faces Edges and Vertices”.

1. Name all the adjacent angles of the given quadrilateral.

a) ∠A, ∠C; ∠B, ∠D
b) ∠A, ∠C
c) ∠A, ∠B; ∠A, ∠D; ∠B, ∠C; ∠C, ∠D
d) ∠A, ∠B; ∠A, ∠D
View Answer

Answer: c
Explanation: Two angles of a quadrilateral which have a common side as an arm are called adjacent angles. ∠A, ∠B; ∠A, ∠D; ∠B, ∠C; ∠C, ∠D are the adjacent angles of the given quadrilateral.
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2. Which of the following are the opposite angles of the given quadrilateral?

a) ∠A, ∠B; ∠A, ∠D; ∠B, ∠C; ∠C, ∠D
b) ∠A, ∠C; ∠B, ∠D
c) ∠A, ∠B
d) ∠A, ∠D; ∠B, ∠C
View Answer

Answer: b
Explanation: Two angles of a quadrilateral which are not adjacent angles are opposite angles.
∠A, ∠C; ∠B, ∠D are the opposite angles of the quadrilateral.

3. Match the following:

     A            B
   1. Adjacent angles      a. ∠X, ∠Y
   2. Opposite angle       b. ∠Y, ∠Z
              c. ∠A, ∠Y     
              d. ∠A, ∠X  
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a) 1-a, b, d; 2-c
b) 1-a, b; 2-d
c) 1-b, d; 2-c
d) 1-a, b, c; 2-d
View Answer

Answer: a
Explanation: When two angles of a quadrilateral have a common side as an arm, they are called adjacent angles and the non-adjacent angles of a quadrilateral are opposite angles.

4. Match the following:

     A            B
    1. Adjacent sides       a. KL, LM
    2. Opposite sides       b. KL, MN
              c. KN, LM
              d. MN, NK 
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a) 1-b, c; 2-a, d
b) 1-b, d; 2-a, c
c) 1-a, b; 2-c, d
d) 1-a, d; 2-b, c
View Answer

Answer: d
Explanation: Two sides of a quadrilateral having a common end point are called adjacent sides of the quadrilateral. Two sides of a quadrilateral which are not having a common end point are called opposite sides of the quadrilateral.

5. Match the pairs:

     A            B
   1. Adjacent sides        a. ∠D, ∠B
   2. Opposite Angle       b. AB, DA
   3. Opposite Side        c. ∠D, ∠C
   4. Adjacent Angle      d. AB, DC 
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a) 1-c, 2-a, 3-d, 4-b
b) 1-b, 2-c, 3-d, 4-a
c) 1-b, 2-a, 3-d, 4-c
d) 1-c, 2-a, 3-d, 4-b
View Answer

Answer: c
Explanation: Two sides of a quadrilateral having a common end point are called adjacent sides of the quadrilateral. Two sides of a quadrilateral which are not having a common end point are called opposite sides of the quadrilateral. Two angles of a quadrilateral which have a common side as an arm are called adjacent angles. Two angles of a quadrilateral which are not adjacent angles are opposite angles.

6. Which are the interior and exterior points of the quadrilateral?

a) Interior point: L, Exterior point: M
b) Interior Point: P, Exterior point: O
c) Interior point: O, Exterior point: K
d) Interior point: L, Exterior point: O
View Answer

Answer: a
Explanation: Points inside the quadrilateral are called interior points of the quadrilateral. Points outside the quadrilateral are called the exterior points of the quadrilateral.
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7. Find ∠B using the information given in the figure.

a) 10°
b) 100°
c) 110°
d) 50°
View Answer

Answer: b
Explanation: By Angle sum property of Quadrilateral,
∠A + ∠B + ∠C + ∠D = 360°
⇒ 110° + ∠B + 120° + 30° = 360°
⇒ ∠B = 100°.

8. If ∠P + ∠Q = 240 and ∠R = 90, find the remaining angle of the quadrilateral PQRS.
a) 30°
b) 40°
c) 50°
d) 60°
View Answer

Answer: a
Explanation: By Angle sum property of Quadrilateral,
∠P + ∠Q + ∠R + ∠S = 360°
240° + 90° + ∠S = 360°
⇒ ∠S = 30°.

9. Find the value of ∠N from the given figure.

a) 110°
b) 30°
c) 90°
d) 100°
View Answer

Answer: d
Explanation: Sum of interior angles of a pentagon is 540°
⇒ ∠K + ∠L + ∠M + ∠N + ∠O = 540°
⇒ ∠O = 540° – 440°
⇒ ∠O = 100°.

10. Find the remaining angle of the given figure.

a) 260°
b) 270°
c) 300°
d) 290°
View Answer

Answer: d
Explanation: Sum of interior angles of a hexagon is 720°
⇒ ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 720°
⇒ ∠F = 720° – 43°
⇒ ∠F = 290°.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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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