Chapter 2 Lines and Angles – Practice set 5

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📘 Practice Set 5

Chapter 2 – Lines and Angles

Practice Set 5 – Part 1
This is the final practice set of the chapter. The questions are completely new and help students revise all important concepts for school examinations, scholarship exams and Olympiads.

Section A – Multiple Choice Questions

  1. Which figure has exactly two endpoints?
    A) Ray    B) Line Segment    C) Line    D) Plane

  2. Which angle measures exactly one-fourth of a complete angle?
    A) Acute Angle    B) Right Angle    C) Straight Angle    D) Reflex Angle

  3. Which geometric figure extends endlessly in all directions on a flat surface?
    A) Line    B) Ray    C) Plane    D) Point

  4. The common point of two rays forming an angle is called the ________.
    A) Arm    B) Vertex    C) Interior    D) Endpoint

  5. Which of the following angles is greater than a straight angle?
    A) Right Angle    B) Acute Angle    C) Reflex Angle    D) Obtuse Angle

  6. Which figure can be represented by two capital letters with arrows on both sides?
    A) Point    B) Line    C) Ray    D) Angle

  7. A point has ________ dimensions.
    A) One    B) Two    C) Three    D) Zero

  8. The measure of a complete angle is ________.
    A) 90°    B) 180°    C) 270°    D) 360°

  9. Which angle is exactly half of a straight angle?
    A) Right Angle    B) Acute Angle    C) Reflex Angle    D) Zero Angle

  10. Which figure is formed when two rays have a common starting point?
    A) Line Segment    B) Plane    C) Angle    D) Line

Section B – Fill in the Blanks

  1. A ray extends endlessly in __________ direction.
  2. A line extends endlessly in __________ directions.
  3. The shortest distance between two points is a __________.
  4. A straight angle measures __________ degrees.
  5. A complete angle measures __________ degrees.
  6. An angle measuring less than 90° is called an __________ angle.
  7. An angle measuring more than 180° but less than 360° is called a __________ angle.
  8. The common point of the two arms of an angle is called the __________.
  9. Points lying on the same straight line are called __________ points.
  10. A plane has length and __________.

Section C – True or False

  1. A line has no endpoints.
  2. A line segment extends endlessly in both directions.
  3. A right angle measures exactly 90°.
  4. A complete angle measures 180°.
  5. A point shows only the position of an object.
  6. A reflex angle is greater than 180°.
  7. Every acute angle is smaller than a right angle.
  8. A plane is a flat surface.
  9. Two opposite rays form a straight angle.
  10. The measure of an angle depends only on the opening between its arms.

✅ Solutions

Section A Answers

  1. B) Line Segment
  2. B) Right Angle
  3. C) Plane
  4. B) Vertex
  5. C) Reflex Angle
  6. B) Line
  7. D) Zero
  8. D) 360°
  9. A) Right Angle
  10. C) Angle

Section B Answers

  1. one
  2. both
  3. line segment
  4. 180
  5. 360
  6. acute
  7. reflex
  8. vertex
  9. collinear
  10. width

Section C Answers

  1. True
  2. False
  3. True
  4. False
  5. True
  6. True
  7. True
  8. True
  9. True
  10. True
🎯 Learning Outcome
  • Students revise all basic geometric figures.
  • Students confidently identify different types of angles.
  • Students strengthen their understanding through fresh, non-repetitive questions.
  • This final practice set helps students prepare for school examinations and competitive exams.

📘 Practice Set 5

Chapter 2 – Lines and Angles

Practice Set 5 – Part 2
This section strengthens your understanding of geometric concepts, properties of angles and classification skills through completely new questions.

Section D – Match the Pairs

Match Column A with the correct answer from Column B.

Column A Column B
1. Acute Angle a. Exactly 360°
2. Line Segment b. One starting point
3. Plane c. Less than 90°
4. Ray d. Flat surface
5. Complete Angle e. Shortest path joining two points
6. Vertex f. Common point of two rays
7. Non-collinear Points g. Points not lying on one straight line
8. Straight Angle h. Exactly 180°
✍️ Write your answers like:
1-__, 2-__, 3-__, 4-__, 5-__, 6-__, 7-__, 8-__

Section E – Identify the Geometric Concept

  1. The edge of a scale joining two corners. __________________

  2. The beam of light from a projector. __________________

  3. A tiny dot marking a village on a map. __________________

  4. The smooth surface of a classroom wall. __________________

  5. An endless straight road imagined in Geometry. __________________

  6. The meeting point of the two hands of a clock. __________________

  7. The space between the two arms of an angle. __________________

  8. The region outside the arms of an angle. __________________

  9. Five points lying on one straight line. __________________

  10. Five points that do not lie on one straight line. __________________

Section F – Identify the Type of Angle

Angle Type of Angle
5°________________
48°________________
90°________________
156°________________
179°________________
180°________________
225°________________
315°________________
0°________________
360°________________

✅ Solutions

Section D Answers

1-c, 2-e, 3-d, 4-b, 5-a, 6-f, 7-g, 8-h

Section E Answers

  1. Line Segment
  2. Ray
  3. Point
  4. Plane
  5. Line
  6. Vertex
  7. Interior of an Angle
  8. Exterior of an Angle
  9. Collinear Points
  10. Non-collinear Points

Section F Answers

Angle Answer
5°Acute Angle
48°Acute Angle
90°Right Angle
156°Obtuse Angle
179°Obtuse Angle
180°Straight Angle
225°Reflex Angle
315°Reflex Angle
0°Zero Angle
360°Complete Angle
🎯 Learning Outcome
  • Students revise all geometric concepts through real-life examples.
  • Students confidently identify every type of angle.
  • Students strengthen logical thinking with a properly shuffled matching exercise.
  • All questions are unique and different from Practice Sets 1, 2, 3 and 4.

📘 Practice Set 5

Chapter 2 – Lines and Angles

Practice Set 5 – Part 3
This part contains observation-based questions, one-sentence answers, conceptual questions and drawing activities.

Section G – Observe and Answer

Study the following imaginary figure carefully.

Five rays start from the common point O:

  • Ray OA points towards the right.
  • Ray OB points diagonally upwards towards the right.
  • Ray OC points straight upwards.
  • Ray OD points towards the left.
  • Ray OE points straight downwards.
  1. What is the common starting point of all the rays?

  2. How many rays are present in the figure?

  3. Name the angle formed by ray OA and ray OB.

  4. What type of angle is ∠AOB?

  5. Name one right angle from the given information.

  6. Name one straight angle.

  7. Which ray is opposite to ray OC?

  8. Name one obtuse angle.

Section H – Answer in One Sentence

  1. Why is a point called a zero-dimensional concept?

  2. What do the arrowheads at both ends of a line show?

  3. Why can the length of a line segment be measured?

  4. How is ray XY named correctly?

  5. What is meant by a point lying on an angle?

  6. Which angle is formed by one-quarter turn?

  7. What type of angle is formed by three-quarter turn?

  8. What is the angle between two adjacent numbers on a clock?

  9. How many right angles make a straight angle?

  10. Can three collinear points form a triangle?

Section I – Short Answer Questions

  1. Explain why only one line can pass through two distinct points.

  2. Write any three differences between a line, a ray and a line segment.

  3. Explain how points on a map help us understand the geometrical meaning of a point.

  4. Why should the vertex be written in the middle while naming an angle with three letters?

  5. Explain how the hands of a clock help us understand different types of angles.

  6. What happens to the number of angles when more rays are drawn from one common point?

  7. Differentiate between points lying inside, outside and on an angle.

  8. Why is the larger angle at 8:00 called a reflex angle?

Section J – Draw and Label

✏️ Draw every figure neatly. Use capital letters for points and show arrowheads correctly.
  1. Draw three collinear points A, B and C.

  2. Draw three non-collinear points P, Q and R.

  3. Draw line XY and mark point M on it.

  4. Draw ray AB and mark point C on the ray after B.

  5. Draw ∠PQR measuring approximately 60°.

  6. Draw ∠ABC measuring approximately 120°.

  7. Draw ∠XYZ measuring 180°.

  8. Draw a reflex angle of approximately 300°.

✅ Solutions

Section G Answers

  1. Point O
  2. 5 rays
  3. ∠AOB
  4. Acute angle
  5. ∠AOC is a right angle.
  6. ∠AOD is a straight angle.
  7. Ray OE
  8. ∠BOD is an obtuse angle.

Section H Answers

  1. A point has no length, width or thickness, so it has zero dimensions.
  2. They show that the line continues endlessly in both directions.
  3. A line segment has two fixed endpoints, so its length can be measured.
  4. It is named from its starting point X through point Y as ray XY.
  5. It means the point lies exactly on one of the arms or at the vertex of the angle.
  6. A right angle.
  7. A reflex angle of 270°.
  8. 30°.
  9. Two right angles.
  10. No. Three collinear points lie on one straight line and cannot form a triangle.

Section I Answers

  1. Two distinct points fix one exact straight direction. Therefore, only one straight line can pass through both points.
  2. A line has no endpoints and extends in both directions. A ray has one starting point and extends in one direction. A line segment has two endpoints and a fixed length.
  3. A city or place on a map is shown by a small dot. That dot shows its exact location, just as a point shows an exact position in Geometry.
  4. The middle letter tells us the common point where the two arms meet. Therefore, it clearly identifies the vertex.
  5. As the clock hands move, they form acute, right, obtuse, straight, reflex and zero angles at different times.
  6. The number of possible angles increases because each new ray can combine with the rays already present.
  7. Interior points lie between the arms, exterior points lie outside the opening, and points on the angle lie exactly on an arm or at the vertex.
  8. At 8:00, the larger angle between the hands is 240°. Since it is greater than 180° but less than 360°, it is a reflex angle.

Section J – Drawing Guidance

  • Q1: Draw one straight line and mark A, B and C on it.
  • Q2: Mark P, Q and R in different positions so that no one line passes through all three.
  • Q3: Draw a line with arrows at both ends, name it XY and place M on it.
  • Q4: Start ray AB from A, pass it through B and mark C after B.
  • Q5: Draw an acute angle of about 60° with Q as the vertex.
  • Q6: Draw an obtuse angle of about 120° with B as the vertex.
  • Q7: Draw two opposite rays with Y as the vertex to form 180°.
  • Q8: Draw and mark the larger outside opening as approximately 300°.

🎯 Learning Outcome

  • Students can study a described figure and identify rays and angles.
  • Students can explain important geometrical concepts clearly.
  • Students can distinguish collinear and non-collinear points.
  • Students can draw and label lines, rays, points and different angles correctly.

📘 Practice Set 5

Chapter 2 – Lines and Angles

Practice Set 5 – Part 4
This final part contains competency-based questions, HOTS, competitive-exam questions and a complete answer key.

⭐ Section K – HOTS Questions

  1. Riya draws two line segments of different lengths, but both form the same opening with another ray. Will the measures of the two angles be equal? Give a reason.

  2. Points A, B and C lie on one straight line, with B between A and C. What angle is formed by ray BA and ray BC? Explain.

  3. A student writes ray PQ as ray QP. Is this always correct? Explain.

  4. Can the same three points be collinear in one diagram and non-collinear in another diagram? Explain.

  5. Why can infinitely many lines pass through one point, but only one line can pass through two distinct points?

  6. Five rays start from one common point. Without drawing, find the total number of different smaller and larger angle pairs formed by choosing any two rays.

  7. An angle is 1° less than a right angle. Name its type. What will its measure be?

  8. An angle is 1° more than a straight angle. Name its type. What will its measure be?

  9. Can a point be both an interior point and a point on the arm of the same angle? Give a reason.

  10. Two angles have arms of different lengths, but both measure 70°. Are the angles equal in measure? Explain.

🏆 Section L – Competitive and Olympiad Questions

  1. Six rays start from one common point. How many different angles can be named by choosing any two rays?
    A) 6    B) 12    C) 15    D) 18

  2. Seven rays start from one point. How many different pairs of rays can be selected?
    A) 14    B) 21    C) 28    D) 35

  3. An angle is three times 30°. What type of angle is it?
    A) Acute    B) Right    C) Obtuse    D) Straight

  4. An angle is five times 45°. What type of angle is it?
    A) Right    B) Obtuse    C) Straight    D) Reflex

  5. What is the smaller angle between the hands of a clock at 5:00?
    A) 120°    B) 150°    C) 180°    D) 210°

  6. What is the larger angle between the hands of a clock at 10:00?
    A) 60°    B) 120°    C) 240°    D) 300°

  7. A complete angle is divided into eight equal parts. What is the measure of each part?
    A) 30°    B) 40°    C) 45°    D) 60°

  8. A straight angle is divided into four equal parts. What is the measure of each part?
    A) 30°    B) 45°    C) 60°    D) 90°

  9. Which one is correctly named if O is the vertex?
    A) ∠OAB    B) ∠AOB    C) ∠ABO    D) ∠AOPB

  10. Which statement is correct?
    A) Every obtuse angle is a reflex angle.
    B) Every right angle is acute.
    C) Every 179° angle is obtuse.
    D) Every 180° angle is reflex.

  11. How many 30° angles together make a straight angle?
    A) 3    B) 4    C) 5    D) 6

  12. How many 45° angles together make a complete angle?
    A) 4    B) 6    C) 8    D) 10

📚 Section M – Competency-Based Case Study

Read the situation carefully.

A teacher marks point O on the board. She draws four rays:

  • Ray OA points towards 12 on an imaginary clock.
  • Ray OB points towards 3.
  • Ray OC points towards 6.
  • Ray OD points towards 9.
  1. Name the angle formed by ray OA and ray OB.
  2. What type of angle is ∠AOB?
  3. Name the angle formed by ray OA and ray OC.
  4. What type of angle is ∠AOC?
  5. Name any one right angle other than ∠AOB.
  6. How many rays have point O as their starting point?
  7. Which ray is opposite to ray OA?
  8. Which ray is opposite to ray OB?

🧠 Section N – Challenge Yourself

  1. Draw four non-collinear points. Join every pair of points with a line segment. How many line segments are formed?
  2. Draw five points on one straight line. How many different line segments can be named by selecting any two points?
  3. An angle is greater than 90° but becomes a straight angle when 50° is added to it. Find the original angle and name its type.
  4. An angle becomes a complete angle when 120° is added to it. Find the original angle and name its type.
  5. Write the names of all seven types of angles in increasing order of their measures.
  6. Explain why 90°, 180° and 360° belong to different angle types even though each is a multiple of 90°.

✅ Solutions

⭐ Section K Answers

  1. Yes. The angles will be equal because the measure of an angle depends on the opening between its arms, not on the lengths of the arms.
  2. A straight angle is formed. Ray BA and ray BC are opposite rays, so the angle measures 180°.
  3. No. Ray PQ starts from P and passes through Q, while ray QP starts from Q and passes through P. Their starting points are different.
  4. Yes. Their positions may be changed in another diagram. If they lie on one straight line, they are collinear; otherwise, they are non-collinear.
  5. A line through one point can be turned in endlessly many directions. Two distinct points fix one exact straight direction, so only one line passes through both.
  6. 10 angles. The number of pairs is:
    5 × 4 ÷ 2 = 10.
  7. It measures 89° and is an acute angle.
  8. It measures 181° and is a reflex angle.
  9. No. A point on an arm lies on the boundary of the angle, while an interior point lies between the arms.
  10. Yes. Both measure 70°, so they are equal in measure even though their arms have different lengths.

🏆 Section L Answers

  1. C) 15
    6 × 5 ÷ 2 = 15
  2. B) 21
    7 × 6 ÷ 2 = 21
  3. B) Right angle
    3 × 30° = 90°
  4. D) Reflex angle
    5 × 45° = 225°
  5. B) 150°
  6. D) 300°
    The smaller angle is 60°, so the larger angle is 360° − 60° = 300°.
  7. C) 45°
    360° ÷ 8 = 45°
  8. B) 45°
    180° ÷ 4 = 45°
  9. B) ∠AOB
    The vertex O is written in the middle.
  10. C) Every 179° angle is obtuse.
  11. D) 6
    180° ÷ 30° = 6
  12. C) 8
    360° ÷ 45° = 8

📚 Section M Answers

  1. ∠AOB
  2. Right angle
  3. ∠AOC
  4. Straight angle
  5. Any one: ∠BOC, ∠COD or ∠DOA
  6. 4 rays
  7. Ray OC
  8. Ray OD

🧠 Section N – Suggested Answers

  1. 6 line segments
    The possible pairs are AB, AC, AD, BC, BD and CD.
  2. 10 line segments
    5 × 4 ÷ 2 = 10
  3. Original angle = 180° − 50° = 130°.
    It is an obtuse angle.
  4. Original angle = 360° − 120° = 240°.
    It is a reflex angle.
  5. Zero angle → Acute angle → Right angle → Obtuse angle → Straight angle → Reflex angle → Complete angle
  6. 90° is a right angle, 180° is a straight angle and 360° is a complete angle because each exact measure represents a different amount of rotation.

🎉 Practice Set 5 Completed Successfully

  • ✅ Basic geometry concepts revised
  • ✅ Point, line, ray, segment and plane covered
  • ✅ Collinear and non-collinear points covered
  • ✅ Interior, exterior and points on an angle covered
  • ✅ All seven angle types covered
  • ✅ Clock-based angle questions included
  • ✅ Competency-based case study included
  • ✅ HOTS and Olympiad questions included
  • ✅ Solutions cross-checked

Students have now completed all five practice sets for Chapter 2 – Lines and Angles.

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