Last Updated on August 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 9 maths. In this article, you will find case study questions for CBSE Class 9 Maths Chapter 6 Lines and Angles. It is a part ofÂ Case Study Questions for CBSE Class 9 MathsÂ Series.

Chapter | Lines and Angles |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 9 |

Subject | Maths |

Useful for | Class 9 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 9 Maths Chapterwise Case Study |

### Case Study Questions on Lines and Angles

**Questions**

A math’s teacher was teaching students about intersecting lines.

Suppose ABÂ and CDÂ are two intersecting lines, which meets at point O. In this point O, she draw a line OEÂ and all these lines were making different angles with each other.

After explaining the description of the figure, she asked the following questions from the students.

On the basis of the above information, solve the following questions.

Q 1. Find the measure of âˆ BOD.

Q 2. Check whether pair of angles âˆ AOCÂ and âˆ BOCÂ makes a linear pair.

Q 3. Which of the following angles form a non collinear lines?

(i) A, O, B

(ii) C, O, E

Q 4. Find the measure of âˆ AOE.

**Solutions**

1. From figure,

$$

\angle B O D=\angle A O C=35^{\circ}

$$

[Vertically opposite angles]

2. From figure, it is clear that

$$

\angle A O C+\angle B O C=180^{\circ}

$$

$[\because A B$ is a straight line $]$

Hence, $\angle A O C$ and $\angle B O C$ makes a linear pair.

3. (i) It is clear from the figure that points $A, O$ and $B$ form a collinear points.

(ii) It is clear from the figure that points $\mathrm{C}, \mathrm{O}, \mathrm{E}$ forms a non-collinear points.

Hence, points C, O, E form a non-collinear line.

4. From the given figure, $C D$ is a line segment.

Therefore, the sum of all angles of the same side of a line is $180^{\circ}$.

$$

\begin{aligned}

& \therefore \angle \mathrm{COA}+\angle \mathrm{AOE}+\angle \mathrm{EOD}=180^{\circ} \\

& \Rightarrow 35^{\circ}+\angle A O E+75^{\circ}=180^{\circ} \\

& \Rightarrow \angle \mathrm{AOE}=180^{\circ}-110^{\circ} \\

& =70^{\circ}

\end{aligned}

$$

### Understanding Lines and Angles

**Line:** A geometrical object that is straight and extends indefinitely in both directions.**Line Segment: **A part of a line with two end points.**Ray: **A part of line with one end point.**Collinear Points:** Three or more points lying on the same line are known as collinear points. Otherwise, they are non-collinear points.**Angle:** It is formed when two rays originate from the same end point. The rays are called arms and the end point is called vertex.

**Types of Angles:**

**Acute Angle:**An angle with measure more than 0Â° but less than 90Â°. In figure, âˆ AOB is acute angle.**Obtuse Angle:**An angle with measure more than 90Â° but less than 180Â°. In figure, âˆ AOD is obtuse angle.**Right Angle:**An angle with measure exactly 90Â°. In figure, âˆ AOC is right angle.**Straight Angle:**An angle with measure 180Â°. In figure, âˆ AOE is straight angle.**Reflex Angle:**An angle with measure more than 180Â° but less than 360Â°. In figure, âˆ AOF is reflex angle, when measured anticlockwise.**Complete Angle:**An angle with measure 360Â°. In figure, âˆ AOA is complete angle.

**Pair of Angles:**

**Complementary Angles:**Two angles with the sum of 90Â°. In above figure, âˆ AOB + âˆ BOC = 90Â°, so âˆ AOB and âˆ BOC are complementary angles.**Supplementary Angles:**Two angles with the sum of 180Â°. In above figure, âˆ AOB + âˆ BOE = 180Â°, so âˆ AOB and âˆ BOE are supplementary angles**Adjacent Angles:**Two angles having a common vertex and a common arm with uncommon arms on either side of the common arm. In figure, âˆ AOC and âˆ BOC are adjacent angles. OR When two angles are adjacent, then their sum is always equal to the angle formed by the two non-common arms. In figure, âˆ AOB = âˆ AOC + âˆ BOC**Linear Pair of Angles:**Two adjacent angles with the sum of 180Â°. In figure, âˆ AOC and âˆ BOC are linear pair of angles.

**Vertically Opposite Angles:** The pair of angles lying on the opposite sides of the point of intersection. In figure, (âˆ AOC and âˆ BOD) and

(âˆ AOD and âˆ BOC) are pairs of vertically opposite angles.

**Bisector of an Angle: **A ray which divides an angle into two equal parts.

### Also check

- Heron’s Formula Class 9 Case Study Questions Maths Chapter 10
- Circles Class 9 Case Study Questions Maths Chapter 9
- Quadrilaterals Class 9 Case Study Questions Maths Chapter 8
- Triangles Class 9 Case Study Questions Maths Chapter 7
- Lines and Angles Class 9 Case Study Questions Maths Chapter 6
- Introduction to Euclidâ€™s Geometry Class 9 Case Study Questions Maths Chapter 5
- Linear Equations in Two Variables Class 9 Case Study Questions Maths Chapter 4
- Coordinate Geometry Class 9 Case Study Questions Maths Chapter 3
- PolynomialsÂ Class 9 Case Study Questions Maths Chapter 2
- Number SystemsÂ Class 9 Case Study Questions Maths Chapter 1

### Topics from which case study questions may be asked

- Basic Terms and Definitions
- Types of Angles
- Intersecting Lines and Non-Intersecting Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Angle Sum Property of a Triangle

The length of perpendiculars at different points on the parallel lines is same.

Case study questions from the above given topic may be asked.

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### Frequently Asked Questions (FAQs) on Lines and Angles Case Study

#### Q1: What are the different types of angles?

A1: Angles are classified based on their measures:**Acute Angle**: Measures less than 90Â°.**Right Angle**: Measures exactly 90Â°.**Obtuse Angle**: Measures more than 90Â° but less than 180Â°.**Straight Angle**: Measures exactly 180Â°.**Reflex Angle**: Measures more than 180Â° but less than 360Â°.

#### Q2: What are complementary and supplementary angles?

A2: **Complementary Angles**: Two angles are complementary if their sum is 90Â°.**Supplementary Angles**: Two angles are supplementary if their sum is 180Â°.

#### Q3: **What is a linear pair of angles?**

A3: A linear pair of angles is formed when two adjacent angles add up to 180Â°. The angles in a linear pair are always supplementary.

#### Q4: **What is the Angle Sum Property of a Triangle?**

A4: The Angle Sum Property states that the sum of the interior angles of a triangle is always 180Â°.

#### Q5: What are parallel lines and a transversal?

A5: **Parallel Lines**: Two lines that are equidistant from each other and never intersect.**Transversal**: A line that intersects two or more lines at distinct points. When a transversal cuts through parallel lines, it forms angles with specific relationships, like corresponding, alternate interior, and alternate exterior angles.

#### Q6: **What is the significance of corresponding angles when a transversal intersects parallel lines?**

A6: When a transversal intersects two parallel lines, the corresponding angles formed are equal. This property helps in proving that the lines are parallel and in solving various geometrical problems.

#### Q7: **Are there any online resources or tools available for practicing Lines and Angles case study questions?**

A8: We provide case study questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.