Chapter 2 Lines and Angles – Exercise

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📘 Exercise 2 – Solutions

Chapter 2 – Lines and Angles

📖 Part 1: This section includes Q1 Choose the correct option and Q2 Match the pairs.

✅ Q1. Choose the Correct Option

i) A complete angle contains .......... right angles.
(a) 1    (b) 2    (c) 3    (d) 4

A complete angle measures 360°. One right angle measures 90°.

So, 360° ÷ 90° = 4.

✅ Answer: (d) 4
ii) If a straight angle is divided into three equal parts, each resulting angle will be ....
(a) zero angle    (b) acute angle    (c) obtuse angle    (d) right angle

A straight angle measures 180°.

If it is divided into three equal parts:

180° ÷ 3 = 60°

An angle of 60° is an acute angle because it is greater than 0° and less than 90°.

✅ Answer: (b) acute angle
iii) The starting point of ray OP and ray OQ is ..........
(a) O    (b) P    (c) Q    (d) P and Q

In a ray, the first letter shows the starting point.

In ray OP, the starting point is O. In ray OQ, the starting point is also O.

✅ Answer: (a) O
iv) ..... is infinite on both sides.
(a) Line    (b) Line segment    (c) Ray    (d) Plane

A line extends endlessly in both directions.

A line segment has two endpoints. A ray extends in only one direction. Therefore, the correct answer is line.

✅ Answer: (a) Line

✅ Q2. Match the Pairs

Group A Group B Correct Match
i) 91° Obtuse angle i - e
ii) 180° Straight angle ii - a
iii) 360° Complete angle iii - b
iv) 215° Reflex angle iv - c
v) 90° Right angle v - d

Explanation

  • 91° is greater than 90° and less than 180°, so it is an obtuse angle.
  • 180° is a straight angle.
  • 360° is a complete angle.
  • 215° is greater than 180° and less than 360°, so it is a reflex angle.
  • 90° is a right angle.
⭐ Final Answers:
i - e, ii - a, iii - b, iv - c, v - d

📘 Exercise 2 – Solutions

Part 2 – Question 3

📖 Question 3: Write the answers by looking at the figure.

(i) Write the names of all the rays in the figure.

A ray starts from one point and extends endlessly in one direction. The arrowhead shows the direction in which the ray continues.

Looking carefully at the figure, the rays are:

  • ➡ Ray DA
  • ➡ Ray EP
  • ➡ Ray EQ
  • ➡ Ray EC
  • ➡ Ray EF
  • ➡ Ray EB
✅ Answer:
Ray DA, Ray EP, Ray EQ, Ray EC, Ray EF and Ray EB.

(ii) On which lines is point E located?

Point E is the common point where different lines meet.

It lies on:

  • 📏 Line PQ
  • 📏 Line CF
  • 📏 Line BE (Ray EB)
💡 In the textbook, students are generally expected to write the complete lines shown. Hence the correct answer is: Line PQ and Line CF.
✅ Answer:
Point E is located on Line PQ and Line CF.

(iii) Write the names of the line segments in the figure.

A line segment has two fixed endpoints.

The line segments visible in the figure are:

  • DE
  • EP
  • EQ
  • EC
  • EF
  • EB
  • DA
✅ Answer:
DE, EP, EQ, EC, EF, EB and DA.

(iv) Write the names of the rays whose starting point is E.

Only the rays that start from point E should be written.

  • ➡ Ray EP
  • ➡ Ray EQ
  • ➡ Ray EC
  • ➡ Ray EF
  • ➡ Ray EB
✅ Answer:
Ray EP, Ray EQ, Ray EC, Ray EF and Ray EB.

(v) What type of angle is ∠BEQ? Write the names of its sides.

The vertex of the angle is E.

One side is Ray EB and the other side is Ray EQ.

The angle is greater than 90° but less than 180°.

💡 Any angle greater than 90° but less than 180° is called an Obtuse Angle.
>
Question Answer
Type of ∠BEQ Obtuse Angle
Sides (Arms) Ray EB and Ray EQ

🌟 Final Answers – Question 3

  1. Rays: Ray DA, Ray EP, Ray EQ, Ray EC, Ray EF, Ray EB.
  2. Point E lies on: Line PQ and Line CF.
  3. Line Segments: DE, EP, EQ, EC, EF, EB and DA.
  4. Rays starting from E: EP, EQ, EC, EF and EB.
  5. ∠BEQ: Obtuse Angle.
    Arms: Ray EB and Ray EQ.

📘 Exercise 2 – Solutions

Part 3 – Questions 4 to 6

📖 This part includes Q4, Q5, Q6, Activity and Use of ICT.

✅ Q4. Write the names and types of the angles in the diagram.

In the figure, all rays start from point O. So, O is the vertex of all angles.

Angle Type of Angle
∠POQ Obtuse Angle
∠QOR Acute Angle
∠ROS Right Angle
∠SOP Obtuse Angle
✅ Answer: ∠POQ – Obtuse angle, ∠QOR – Acute angle, ∠ROS – Right angle, ∠SOP – Obtuse angle.

✅ Q5. Find the number of acute angles.

Observe the given series of triangle figures. By counting all the acute angles formed in each figure, the number of acute angles increases by 9 each time.

Figure Number of Acute Angles
(a) 3
(b) 12
(c) 21
(d) 30
⭐ Pattern: 3, 12, 21, 30
The number of acute angles increases by 9 each time.

✅ Q6. Draw a freehand picture.

Students can draw any simple picture using:

  • Acute angle
  • Right angle
  • Obtuse angle
✅ Example: A house picture can be drawn. The roof may show acute angles, the wall corners may show right angles, and an open door may show an obtuse angle.

🎯 Activity

Activity: List the angles in objects found in the surrounding. Classify them according to their types.
Object Type of Angle
Corner of a book Right Angle
Slightly open scissors Acute Angle
Wide open door Obtuse Angle
Straight road Straight Angle

💻 Use of ICT

Students can use GEOGEBRA to draw points, lines, line segments, planes, rays and angles.

🌟 Final Summary

  • Q4 asks us to identify angle names and their types.
  • Q5 follows the pattern 3, 12, 21, 30.
  • Q6 is a drawing activity using different types of angles.
  • Angles can be found in many objects around us.

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