This MCQ module is based on: Types of Angles and Chapter Exercises
TOPIC 7 OF 41
Types of Angles and Chapter Exercises
🎓 Class 6
Mathematics
CBSE
Theory
Ch 2 — Lines and Angles
⏱ ~40 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Types of Angles and Chapter Exercises
Targeting Class 6 level in Geometry, with Basic difficulty.
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2.11 Types of Angles and their Measures
Now that we can measure angles using a protractor, we can classify angles into different types based on their degree measure.
Acute Angle (less than 90°)
An acute angle? is any angle that measures greater than 0° and less than 90°. The word "acute" means sharp — these angles look sharp and pointy.
Examples of Acute Angles
All acute angles: 0° < angle < 90°
Obtuse Angle (between 90° and 180°)
An obtuse angle? is any angle that measures greater than 90° and less than 180°. The word "obtuse" means blunt — these angles look wide and blunt.
Examples of Obtuse Angles
All obtuse angles: 90° < angle < 180°
Reflex Angle (between 180° and 360°)
A reflex angle? is any angle that measures greater than 180° and less than 360°. When you see two rays forming an angle, there is always a smaller angle and a larger (reflex) angle on the other side. The reflex angle is the one that goes the "long way round."
Reflex Angle — 270° Example
The small angle is 90° (right angle). The reflex angle on the other side is 360° − 90° = 270°.
⚠️ Key Relationship
For any two rays from a common vertex, the smaller angle + reflex angle = 360° (a full turn). So if the smaller angle is \(x°\), the reflex angle is \((360 - x)°\).
Summary of All Angle Types
Acute Angle
0° < angle < 90°
Sharp, pointy opening
Sharp, pointy opening
Right Angle
Exactly 90°
Marked with □ symbol
Marked with □ symbol
Obtuse Angle
90° < angle < 180°
Wide, blunt opening
Wide, blunt opening
Straight Angle
Exactly 180°
Arms form a straight line
Arms form a straight line
Reflex Angle
180° < angle < 360°
Goes the "long way round"
Goes the "long way round"
Full Turn
Exactly 360°
Complete rotation
Complete rotation
| Angle Type | Measure | Example |
|---|---|---|
| Zero angle | 0° | Arms overlap completely |
| Acute angle | 0° < x < 90° | 30°, 45°, 60°, 89° |
| Right angle | x = 90° | Corner of a book |
| Obtuse angle | 90° < x < 180° | 110°, 130°, 175° |
| Straight angle | x = 180° | Arms form a line |
| Reflex angle | 180° < x < 360° | 200°, 270°, 350° |
| Full turn | x = 360° | Complete rotation |
Angle Classifier
Bloom: L3 ApplySet any angle from 0° to 360° and see its type and visual:
120°
Figure it Out — Section 2.11 (Pages 51–54)
Q1. Draw: (a) An acute angle (b) An obtuse angle (c) A reflex angle. Mark the intended angles with curves.
Answer: Using a protractor:
(a) Draw any angle less than 90° (e.g., 50°). Mark with a small arc.
(b) Draw any angle between 90° and 180° (e.g., 130°). Mark with a small arc.
(c) Draw two rays forming a small angle, then mark the larger angle on the outside with a big arc. If the small angle is 60°, the reflex angle is 300°.
(a) Draw any angle less than 90° (e.g., 50°). Mark with a small arc.
(b) Draw any angle between 90° and 180° (e.g., 130°). Mark with a small arc.
(c) Draw two rays forming a small angle, then mark the larger angle on the outside with a big arc. If the small angle is 60°, the reflex angle is 300°.
Figure for Q2 — Rays from Vertex T
Measure \(\angle PTR\), \(\angle PTQ\), \(\angle PTW\), \(\angle WTP\) and classify each
Q2. Use a protractor to find the measure of each angle in the figure above. Then classify each as acute, obtuse, right, or reflex: (a) \(\angle PTR\) (b) \(\angle PTQ\) (c) \(\angle PTW\) (d) \(\angle WTP\)
Answer: (Approximate values from the figure — measure precisely with your protractor)
(a) \(\angle PTR \approx 80°\) — Acute
(b) \(\angle PTQ \approx 40°\) — Acute
(c) \(\angle PTW \approx 160°\) — Obtuse
(d) \(\angle WTP \approx 200°\) (reflex, measured the long way) — Reflex. Note: \(\angle WTP\) going the short way = 160° (obtuse), but if measured as the reflex angle = 360° − 160° = 200°.
(a) \(\angle PTR \approx 80°\) — Acute
(b) \(\angle PTQ \approx 40°\) — Acute
(c) \(\angle PTW \approx 160°\) — Obtuse
(d) \(\angle WTP \approx 200°\) (reflex, measured the long way) — Reflex. Note: \(\angle WTP\) going the short way = 160° (obtuse), but if measured as the reflex angle = 360° − 160° = 200°.
Q3. Draw angles with the following degree measures: (a) 140° (b) 82° (c) 195° (d) 70° (e) 35°
Answer: Use the 5-step protractor method for each:
(a) 140° — obtuse angle
(b) 82° — acute angle
(c) 195° — reflex angle. To draw: first draw 360° − 195° = 165° (obtuse), then mark the reflex angle on the other side.
(d) 70° — acute angle
(e) 35° — acute angle
(a) 140° — obtuse angle
(b) 82° — acute angle
(c) 195° — reflex angle. To draw: first draw 360° − 195° = 165° (obtuse), then mark the reflex angle on the other side.
(d) 70° — acute angle
(e) 35° — acute angle
Q4. Draw the letter 'M' such that the angles on the sides are 40° each and the angle in the middle is 60°.
Answer: Draw two vertical strokes. From the top of the left stroke, draw a line going down-right at 40° from vertical. From the top of the right stroke, draw a line going down-left at 40° from vertical. These two lines meet in the middle, forming a 60° angle at the bottom of the 'V' shape. The overall letter looks like M with precisely measured angles.
Q5. Draw the letter 'Y' such that the three angles formed are 150°, 60° and 150°.
Answer: Draw a vertical line downward (the stem). From the top, draw two arms going up-left and up-right. The angle between the left arm and the stem = 150°, the angle between the two upper arms = 60°, and the angle between the right arm and the stem = 150°. Check: 150° + 60° + 150° = 360° (full turn around the junction point).
Ashoka Chakra — 24 Spokes
Q6. The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two adjacent spokes? What is the largest acute angle formed between two spokes?
Answer:
Angle between adjacent spokes = \(\frac{360°}{24} = \mathbf{15°}\).
The largest acute angle must be less than 90°. The largest multiple of 15° less than 90° is \(5 \times 15° = 75°\) (6 spokes apart gives exactly 90° which is not acute).
So the largest acute angle = 75°.
Angle between adjacent spokes = \(\frac{360°}{24} = \mathbf{15°}\).
The largest acute angle must be less than 90°. The largest multiple of 15° less than 90° is \(5 \times 15° = 75°\) (6 spokes apart gives exactly 90° which is not acute).
So the largest acute angle = 75°.
Q7. Puzzle: I am an acute angle. If you double my measure, you get an acute angle. If you triple it, you still get an acute angle. If you quadruple it, you still get an acute angle! But if you multiply my measure by 5, you get an obtuse angle. What are the possible values of my measure?
Answer: Let the angle be \(x°\).
Given: \(x < 90°\), \(2x < 90°\), \(3x < 90°\), \(4x < 90°\), but \(5x > 90°\).
From \(4x < 90°\): \(x < 22.5°\)
From \(5x > 90°\): \(x > 18°\)
So \(18° < x < 22.5°\).
Possible integer values: \(x = 19°, 20°, 21°, 22°\).
Given: \(x < 90°\), \(2x < 90°\), \(3x < 90°\), \(4x < 90°\), but \(5x > 90°\).
From \(4x < 90°\): \(x < 22.5°\)
From \(5x > 90°\): \(x > 18°\)
So \(18° < x < 22.5°\).
Possible integer values: \(x = 19°, 20°, 21°, 22°\).
Chapter 2 — Summary
📖 Key Takeaways
- A point marks a position; a line segment has two endpoints; a line extends infinitely both ways; a ray starts at one point and extends infinitely one way
- An angle is formed by two rays sharing a common starting point (vertex)
- Angles can be compared by superimposition
- The degree (°) is the unit for measuring angles; a full turn = 360°
- A protractor measures angles from 0° to 180°
- Angle types: acute (<90°), right (=90°), obtuse (90°–180°), straight (=180°), reflex (180°–360°)
- Two perpendicular lines meet at 90°
- An angle bisector divides an angle into two equal halves
- Sum of angles in a triangle = 180°; in a quadrilateral = 360°
🔍 Activity 2.4 — Angle Hunt Around You
Bloom: L3 Apply
🤔 PREDICT FIRST: Look around your room. Do you think there are more acute angles, right angles, or obtuse angles in everyday objects?
- Find and list 3 examples each of acute, right, obtuse, and straight angles in your surroundings
- Measure each angle using a protractor (or estimate if you can't reach)
- Classify each angle by type
- Which type appeared most often? Why do you think so?
✅ Observation & Explanation
Right angles are the most common in man-made objects — book corners, door frames, table edges, window panes, screens, tiles. This is because right angles provide stability and symmetry in construction. Acute angles appear in rooftops, arrowheads, and letter shapes like A and V. Obtuse angles appear in reclining chairs, open books, and clock hands at certain times.
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Competency-Based Questions
Scenario: An architect is designing a garden with a circular fountain at the centre. Pathways radiate outward from the fountain like spokes of a wheel, and flower beds fill the spaces between pathways. The architect uses angle measurements to plan the layout.
Q1. The architect places 8 equally spaced pathways. What is the angle between adjacent pathways?
L3 Apply
Answer: (C) 45° — \(\frac{360°}{8} = 45°\) between adjacent pathways.
Q2. A flower bed occupies the space between two pathways that are 3 pathways apart. What angle does this flower bed subtend at the fountain? Classify this angle.
L4 Analyse
Answer: 3 gaps × 45° = 135°. This is an obtuse angle (between 90° and 180°).
Q3. The architect claims: "If I place the pathways at 40° apart, I can fit exactly 9 pathways." Is this claim correct? Justify mathematically.
L5 Evaluate
Answer: \(\frac{360°}{40°} = 9\). Yes, the claim is correct. 9 pathways at 40° apart would use exactly \(9 \times 40° = 360°\), completing the full circle with no gap or overlap.
HOT Q. Design a clock face where each hour mark is 40° apart instead of 30°. How many hour marks would it have? What problems might arise with such a clock?
L6 Create
Hint: At 40° per mark: \(\frac{360°}{40°} = 9\) hour marks. This clock would have a 9-hour cycle instead of 12. Problems: it would not match the standard 24-hour day (24 ÷ 9 is not a whole number), making it impractical. Our 12-hour clock works because 360 ÷ 12 = 30° gives clean divisions, and 24 ÷ 12 = 2 (two cycles per day).
⚖️ Assertion–Reason Questions
Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is NOT the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is NOT the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.
Assertion (A): An angle measuring 200° is a reflex angle.
Reason (R): Reflex angles are those with measures greater than 180° and less than 360°.
Answer: (A) — Both true. 200° falls between 180° and 360°, so it is a reflex angle by definition. R correctly explains this.
Assertion (A): If two angles add up to 360°, they must be supplementary.
Reason (R): Supplementary angles add up to 180°.
Answer: (D) — A is false (supplementary means adding to 180°, not 360°; angles adding to 360° form a complete turn). R is true — supplementary angles do add up to 180°.
Assertion (A): Every pair of rays from a common vertex creates exactly two angles that add up to 360°.
Reason (R): A full rotation around any point equals 360°.
Answer: (A) — Both true. Two rays from a vertex divide the plane into two angles (one smaller, one reflex). Together they always equal a full turn: 360°. R correctly explains why.
Frequently Asked Questions
What are complementary and supplementary angles?
Complementary angles are two angles that add up to 90 degrees. Supplementary angles are two angles that add up to 180 degrees. For example, 30 and 60 degrees are complementary while 120 and 60 degrees are supplementary. These concepts appear in NCERT Class 6 Maths Chapter 2 exercises.
How do you classify an angle by its measure?
Measure the angle using a protractor, then classify it: less than 90 degrees is acute, exactly 90 degrees is a right angle, between 90 and 180 is obtuse, exactly 180 is straight, and between 180 and 360 is reflex. NCERT Class 6 Chapter 2 provides extensive practice on this classification.
What is the sum of angles on a straight line?
The sum of angles on a straight line is always 180 degrees. This is called the straight angle property. If one angle on a straight line is 70 degrees, the other must be 110 degrees because 70 plus 110 equals 180. This property is used in many NCERT Class 6 Chapter 2 exercises.
How to find the complement of an angle?
To find the complement of an angle, subtract it from 90 degrees. For example, the complement of 35 degrees is 90 minus 35, which equals 55 degrees. Note that only angles less than 90 degrees have complements. This is practised in NCERT Class 6 Ganita Prakash Chapter 2 exercises.
What are adjacent angles in Class 6 Maths?
Adjacent angles are two angles that share a common vertex and a common arm but do not overlap. They lie on opposite sides of the common arm. For example, when two lines cross, they form two pairs of adjacent angles. Understanding adjacency helps in solving angle problems in NCERT Class 6 Maths.
Frequently Asked Questions — Lines and Angles
What is Types of Angles and Chapter Exercises in NCERT Class 6 Mathematics?
Types of Angles and Chapter Exercises is a key concept covered in NCERT Class 6 Mathematics, Chapter 2: Lines and Angles. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Types of Angles and Chapter Exercises step by step?
To solve problems on Types of Angles and Chapter Exercises, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 6 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 2: Lines and Angles?
The essential formulas of Chapter 2 (Lines and Angles) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Types of Angles and Chapter Exercises important for the Class 6 board exam?
Types of Angles and Chapter Exercises is part of the NCERT Class 6 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Types of Angles and Chapter Exercises?
Common mistakes in Types of Angles and Chapter Exercises include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Types of Angles and Chapter Exercises?
End-of-chapter NCERT exercises for Types of Angles and Chapter Exercises cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 2, and solve at least one previous-year board paper to consolidate your understanding.
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