ML Aggarwal Rectilinear Figures MCQs Class 9 ICSE Maths Solutions

ML Aggarwal Rectilinear Figures MCQs Class 9 ICSE Maths Solutions Ch-13. Step by Step Solutions of MCQs on Rectilinear Figures of ML Aggarwal for ICSE Class 9th Mathematics. Visit official website CISCE for detail information about ICSE Board Class-9.

ML Aggarwal Rectilinear Figures MCQs Class 9 ICSE Maths Solutions Ch-13

Board ICSE
Subject Maths
Class 9th
Chapter-13 Rectilinear Figures
Topics Solution of MCQs Questions
Academic Session 2024-2025

MCQs on Rectilinear Figures

ML Aggarwal Rectilinear Figures Class 9 ICSE Maths Solutions Ch-13

Question 1. Three angles of a quadrilateral are 75°, 90° and 75°. The fourth angle is

(a) 90°
(b) 95°
(c) 105°
(d) 120°

Answer :  (d) 120° is correct

Hint:  Sum of 4 angles of a quadrilateral = 360° Sum of three angles = 75° + 90° + 75° = 240° Fourth angle = 360° – 240° = 120°

Question 2. A quadrilateral ABCD is a trapezium if

(a) AB = DC
(b) AD = BC
(c) ∠A + ∠C = 180°
(d) ∠B + ∠C = 180°

Answer :  (d) ∠B + ∠C = 180° is correct 

Hint:  A quadrilateral ABCD is a trapezium if ∠B + ∠C= 180°
(Sum of co-interior angles)

Question 3. If PQRS is a parallelogram, then ∠Q – ∠S is equal to

(a) 90°
(b) 120°
(c) 0°
(d) 180°

Answer :  (c) 0° is correct

Hint:   PQRS is a parallelogram ∠Q – ∠S = 0
(∵ Opposite angles of a parallelogram, are equal) 

Question 4. A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is

(a) 55°
(b) 50°
(c) 40°
(d) 25°

Answer :  (b) 50° is correct 

Hint:    In a rectangle a diagonal is inclined to one side of the rectangle is 25°

In ΔOCD,

∠ODC + ∠OCD + ∠COD = 180°

⇒ 25° + 25° + ∠COD = 180°

⇒ ∠COD = 130°

Acute angle i.e. ∠DOA between the diagonals

= 180° – ∠DOC

= 180° – 130° = 50°

Question 5. ABCD is a rhombus such that ∠ACB = 40°. Then ∠ADB is

(a) 40°
(b) 45°
(c) 50°
(d) 60°

Answer :  (c) 50° is correct

Hint:  According to the question,

ABCD is a rhombus

∠ACB = 40°

ABCD is a rhombus such that ∠ACB = 40°. Then ∠ADB is

∵ ∠ACB = 40°

⇒ ∠OCB = 40°

∵ AD ∥ BC

⇒ ∠DAC = ∠BCA = 40° [Alternate interior angles]

⇒ ∠DAO = 40° Since, diagonals of a rhombus are perpendicular to each other

∠AOD = 90°

Sum of all angles of a triangle = 180°

⇒ ∠AOD + ∠ADO + ∠DAO = 180°

 ⇒ 90° + ∠ADO + 40° = 180°

⇒ 130° + ∠ADO = 180° ⇒ ∠ADO = 180° – 130°

⇒ ∠ADO = 50°

⇒ ∠ADB = 50°

Hence, ∠ADB = 50°

Question 6. The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠D AC = 32° and ∠AOB = 70°, then ∠DBC is equal to

(a) 24°
(b) 86°
(c) 38°
(d) 32°

Answer :  (c) 38° is correct

Hint:    ∠AOB = 70°,  ∠DAC = 32°

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠D AC = 32° and ∠AOB = 70°, then ∠DBC is equal to

∵ AD ∥ BC and AC is transversal

∴ ∠ACB = 32°

∠AOB + ∠BOC = 180°

⇒ 70° + ∠BOC = 180°

⇒ ∠BOC = 180° – 70°

⇒ ∠BOC = 110°

Sum of all angles of a triangle = 180°

⇒ ∠BOC + ∠BCO + ∠OBC = 180°

⇒ 110° + 32°+ ∠OBC = 180°

⇒ 142°+ ∠OBC = 180°

⇒ ∠OBC = 180° – 142°

⇒ ∠OBC = 38°

Hence, ∠DBC = 38°

Question 7. If the diagonals of a square ABCD intersect each other at O, then ∆OAB is

(a) an equilateral triangle
(b) a right angled but not an isosceles triangle
(c) an isosceles but not right angled triangle
(d) an isosceles right angled triangle

Answer :  (d) an isosceles right angled triangle  is correct

Question 8. If the diagonals of a quadrilateral PQRS bisect each other, then the quadrilateral PQRS must be a

(a) parallelogram
(b) rhombus
(c) rectangle
(d) square

Answer :  (a) parallelogram is correct

Hint:   Diagonals of a quadrilateral PQRS bisect each other, then quadrilateral must be a parallelogram.
(∵ A rhombus, rectangle and square are also parallelogram)

Question 9. If the diagonals of a quadrilateral PQRS bisect each other at right angles, then the quadrilateral PQRS must be a

(a) parallelogram
(b) rectangle
(c) rhombus
(d) square

Answer :  (c) rhombus is correct

Diagonals of quadrilateral PQRS bisect each other at right angles, then quadrilateral PQRS [ must be a rhombus.
(∵ Square is also a rhombus with each angle equal to 90°) 

Question 10. Which of the following statement is true for a parallelogram?

(a) Its diagonals are equal.
(b) Its diagonals are perpendicular to each other.
(c) The diagonals divide the parallelogram into four congruent triangles.
(d) The diagonals bisect each other.

Answer : (d) The diagonals bisect each other is correct 

For a parallelogram an the statement ‘The diagonals bisect each other’ is true. 

Question 11. Which of the following is not true for a parallelogram?

(a) opposite sides are equal
(b) opposite angles are equal
(c) opposite angles are bisected by the diagonals
(d) diagonals bisect each other

Answer :  (c) opposite angles are bisected by the diagonals is correct

The statement that in a parallelogram, .the opposite angles are bisected by the diagonals, is not true in each case.

Question 12. A quadrilateral in which the diagonals are equal and bisect each other at right angles is a

(a) rectangle which is not a square
(b) rhombus which is not a square
(c) kite which is not a square
(d) square

Answer : (d) square is correct

Hint:  In a quadrilateral, if diagonals are equal and bisect each other at right angles, is a square. 

—  : End of ML Aggarwal Rectilinear Figures MCQs Class 9 ICSE Maths Solutions :–

Return to :-  ML Aggarawal Maths Solutions for ICSE  Class-9

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