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°

∵ ∠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°

∵ 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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