# 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”. a) ∠A, ∠C; ∠B, ∠D
b) ∠A, ∠C
c) ∠A, ∠B; ∠A, ∠D; ∠B, ∠C; ∠C, ∠D
d) ∠A, ∠B; ∠A, ∠D

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

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

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

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

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

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°

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°

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°

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°

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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