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

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.

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

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

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

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

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

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

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

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

Explanation: Points inside the quadrilateral are called interior points of the quadrilateral. Points outside the quadrilateral are called the exterior points of the quadrilateral.

7. Find ∠B using the information given in the figure.

a) 10°

b) 100°

c) 110°

d) 50°

View Answer

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

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

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

Explanation: Sum of interior angles of a hexagon is 720°

⇒ ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 720°

⇒ ∠F = 720° – 43°

⇒ ∠F = 290°.

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