RD Sharma Solutions Class 6 Maths Chapter 11 Angles – Free PDF Download

RD Sharma Solutions for Class 6 Maths Chapter 11 focuses on the important topic of Maths i.e Angles. This chapter introduces students to the basic concepts of geometry, explaining what an angle is, how it is formed, and the different types of angles such as acute, obtuse, right, straight, and reflex angles. Students also learn how to measure angles using a protractor and identify angles in different shapes and figures, which is a key part of the CBSE syllabus for Class 6.

To gain a solid understanding of angles, it's important for students to practice regularly using the RD Sharma Solutions, which offer step-by-step answers to textbook questions in a clear and simple manner. These solutions are especially useful for quick revision and help build confidence when solving problems involving angle properties and classification.

Students preparing for their school exams or aiming for top performance in CBSE Class 6 Maths can benefit from reliable study resources like the RD Sharma Class 6 Chapter 11 PDF, available on trusted platforms. These solutions not only make learning angles easier but also show how to apply angle knowledge in real-life contexts—like reading a clock, designing, or navigating turns.

RD Sharma Solution for Class 6 Chapter 11 - Download PDF

We’ve provided the complete RD Sharma textbook solutions in a simple, step-by-step format to help students understand and master the concept of angles with ease. These solutions are available in a downloadable PDF format, so you can solve these questions according to your time and even offline. 

Practicing with these RD Sharma Solutions for Class 6 Maths Chapter 11 PDF helps improve accuracy, build confidence, and prepare better for school exams. Whether it’s identifying angle types or measuring them using a protractor, these clear explanations will help students in solving and mastering this chapter.

RD Sharma Solutions Class 6 Maths Chapter 11 Angles - Objective Type

Choose the correct answer for each of the following:

1. What is the measure of a right angle?
(a) 60°
(b) 90°
(c) 120°
(d) 180°

Answer: (b) 90°

2. Which of the following is an acute angle?
(a) 125°
(b) 180°
(c) 85°
(d) 95°

Answer: (c) 85°

3. Which angle is formed when the clock shows 3:00?
(a) Straight angle
(b) Right angle
(c) Obtuse angle
(d) Acute angle

Answer: (b) Right angle

4. A complete angle is equal to:
(a) 180°
(b) 270°
(c) 360°
(d) 90°

Answer: (c) 360°

5. What do we call an angle bigger than 180° but smaller than 360°?
(a) Acute angle
(b) Straight angle
(c) Reflex angle
(d) Obtuse angle

Answer: (c) Reflex angle

6. If the angle between neighboring spokes on a bicycle wheel is 18°, how many spokes does the wheel have?
(a) 18
(b) 24
(c) 30
(d) 36

Answer: (c) 24
(360 ÷ 15 = 24)

7. An angle that exactly divides a straight angle into two equal parts is called:
(a) Zero angle
(b) Obtuse angle
(c) Right angle
(d) Reflex angle

Answer: (c) Right angle
(Half of 180° = 90°)

8. A teacher rotates a pointer on the board from North to East. What type of angle is formed?
(a) Straight angle
(b) Obtuse angle
(c) Right angle
(d) Reflex angle

Answer: (c) Right angle

9. In a triangle where all sides are equal in length, what is the size of each angle?
(a) 45°
(b) 90°
(c) 120°
(d) 60°

Answer: (d) 60°

10. How many 90° angles make up a full circle?
(a) 2
(b) 3
(c) 4
(d) 6

Answer: (c) 4
(360 ÷ 90 = 4)

Word Problems on Angles (Advanced Level with Detailed Answers)

1. Riya is flying a kite. Initially, the thread of the kite makes an angle of 70° with the ground. As the wind direction changes, the thread now makes an angle of 110° with the ground in the opposite direction. Through what angle has the kite thread turned?

Solution:
Initial angle = 70°
Final angle on opposite side = 110°
Total angle turned = 70° + 110° = 180°
The string of the kite rotated halfway around, making a flat line shape (180°).

2. An artist turns while painting a circular mural. She starts facing east and makes a turn of 225° clockwise. In which direction is she facing now?

Solution:
225° clockwise from east means:

90° → South

180° → West

Remaining = 225° − 180° = 45°
So, 45° beyond west = South-West
She is now facing South-West.

3. A rotating sprinkler covers an area in equal angle sections. If it completes one full rotation and sprays 12 equal water streams, what is the angle between two consecutive streams?

Solution:
Total angle in one rotation = 360°
Number of sections = 12
Angle between two consecutive streams = 360° ÷ 12 = 30°
Each angle is 30°.

4. When a wall clock reads exactly 3:00, the minute hand points to 12 and the hour hand points to 3. What time will it be when these two hands first form a right angle (90°) after 3:00?
Solution:
At 3:00, the hands start in different positions.

Minute hand moves at 6° every minute
Hour hand moves at 0.5° every minute

Let's say x minutes pass before they make a 90° angle.
After x minutes:

Minute hand position: 0° + 6°× x
Hour hand position: 90° + 0.5°× x

For a 90° angle between them:
|(0° + 6°× x) - (90° + 0.5°× x)| = 90°
|6°× x - 90° - 0.5°× x| = 90°
|5.5°× x - 90°| = 90°
Since the minute hand moves faster, we get:
5.5°× x - 90° = 90°
5.5°× x = 180°
x = 180° ÷ 5.5° = 32.73 minutes
So the hands form a right angle at approximately 3:32.7, or 3 hours, 32 minutes, and 44 seconds.

5. The hands of a clock are 120° apart. What are the possible times between 12 and 6 when this occurs?

Solution:
Let’s denote:

Angle between hands = |30H − (11/2)M| = 120
Try values for H = 2, 3, 4, etc.

Try H = 4:
|30×4 − (11/2)M| = 120
120 − (11/2)M = 120 → M = 0
Time = 4:00

Try H = 2:
|60 − (11/2)M| = 120
(11/2)M = 60
M = 120 ÷ 11 = 10.91 ≈ 11 minutes
Time ≈ 2:11

Possible times include approximately 2:11 and 4:00.

6. A regular polygon has an exterior angle of 40°. How many sides does it have?

Solution:
Exterior angle = 40°
Number of sides = 360 ÷ Exterior angle
= 360 ÷ 40 = 9
The polygon has 9 sides.

7. Two angles form a linear pair. If one angle is 4 times the other, find both angles.

Solution:
Let the smaller angle be x.
Then the larger angle = 4x
Since they form a linear pair: x + 4x = 180
5x = 180 → x = 36
Larger angle = 4 × 36 = 144
Angles are 36° and 144°.

8. A windmill rotates through 3 full turns and then stops at a point that forms an angle of 60° from its initial position. Through what total angle did it rotate?

Solution:
1 full turn = 360°
3 turns = 3 × 360° = 1080°
Plus 60° extra = 1080° + 60° = 1140°
 Total rotation = 1140°.

9. A sector of a circle has a central angle of 72°. What fraction of the circle’s area does it represent?

Solution:
Fraction = Angle ÷ 360 = 72 ÷ 360 = 1/5
The sector represents one-fifth of the circle’s area.

10. The angles of a triangle are in the ratio 2:3:4. Classify each angle and find their exact measures.

Solution:
Sum of angles in triangle = 180°
Ratio parts = 2 + 3 + 4 = 9
Each part = 180 ÷ 9 = 20

First angle = 2 × 20 = 40° (Acute)

Second angle = 3 × 20 = 60° (Acute)

Third angle = 4 × 20 = 80° (Acute)
All three angles are acute: 40°, 60°, and 80°.