NCERT Solutions for Class 6 Maths Chapter 2 - Lines and Angles Exercise 2.11

Exercise 2.11

1. In each of the below grids, join A to other grid points in the figure by a straight line to get: 

a. An acute angle

b. An obtuse angle

c. A reflex angle

Mark the intended angles with curves to specify the angles. One has been done for you. 

Ans: 

2. Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or reflex. 

a. ∠PTR b. ∠PTQ c. ∠PTW d. ∠WTP

Ans: (a) ∠PTR = 300° is a reflex angle, as it is greater than 180°.
(b) ∠PTQ = 60° is an acute angle because it is less than 90°.
(c) ∠PTW = 105° is an obtuse angle, as it is greater than 90° but less than 180°.
(d) ∠WTP = 225° is a reflex angle, as it exceeds 180°.

Each of these angles has been categorized based on its measurement, showing the differences between acute, obtuse, and reflex angles. These types of angles are important for understanding basic geometry and for practical applications in various real-world contexts.

3. Draw angles with the following degree measures: 

a. 140° b. 82° c. 195° d. 70° e. 35° 

Ans: 

4. Estimate the size of each angle and then measure it with a protractor:

Classify these angles as acute, right, obtuse or reflex angles

Ans: (a) A 45° angle is classified as acute, as it is less than 90°.
(b) A 150° angle is considered obtuse since it is greater than 90° but less than 180°.
(c) A 120° angle is also an obtuse angle, falling between 90° and 180°.
(d) A 30° angle is an acute angle, being smaller than 90°.
(e) A 95° angle is classified as obtuse, as it is slightly greater than 90°.
(f) A 350° angle is a reflex angle, as it is greater than 180° but less than 360°.

Each of these angles demonstrates the different types—acute, obtuse, and reflex—based on their measures. Understanding how to classify angles is an important skill in geometry, helping in tasks like designing, constructing, and analysing shapes in real-life contexts.

5. Make any figure with three acute angles, one right angle and two obtuse angles.

Ans: 

Angles 1, 2, and 3 are classified as acute angles, as each is less than 90°. Angle 4 is a right angle, meaning it measures exactly 90°. Angles 5 and 6 are obtuse, as they are greater than 90° but less than 180°.

These angles cover the basic types commonly seen in geometry—acute, right, and obtuse. Knowing how to identify and classify these angles is essential for understanding geometric shapes and solving problems related to construction, design, and real-world applications of angles.

6. Draw the letter ‘M’ such that the angles on the sides are 40° each and the angle in the middle is 60°.

Ans: 

Angle ∠1 measures 30°, angle ∠2 is also 30°, and angle ∠3 measures 60°. Both ∠1 and ∠2 are acute angles, as they are less than 90°, while ∠3 is slightly larger but still acute, as it is less than 90° as well.

These angles are typical in many geometric shapes, such as triangles. Understanding these different measurements is important for analyzing shapes, solving problems involving angles, and applying these concepts to practical tasks like architecture or engineering.

7. Draw the letter ‘Y’ such that the three angles formed are 150°, 60° and 150°.

Ans:

Angle ∠1 measures 150°, angle ∠2 is 60°, and angle ∠3 is also 150°. Both ∠1 and ∠3 are obtuse angles, as they are greater than 90° but less than 180°, while ∠2 is an acute angle, as it is smaller than 90°.

These angle measures often appear in geometric shapes such as irregular polygons. Understanding the differences between acute and obtuse angles is key for solving geometry problems and applying this knowledge in real-life contexts, such as construction or design.

8. The Ashoka Chakra has 24 spokes. What is the degree measure of the angle between two spokes next to each other? What is the largest acute angle formed between two spokes?

Ans: The angle between two consecutive spokes is calculated as 360° ÷ 24, which equals 15°. The largest acute angle can be found by multiplying 15° by 5, resulting in 75°.

These calculations are useful when analysing symmetrical objects like wheels or gears, where equal spacing is important. Understanding how to divide a circle into equal angles helps in various practical applications, from designing mechanical parts to creating artistic patterns. The largest acute angle in this example, 75°, is commonly seen in many geometric constructions.

9. Puzzle: I am an acute angle. If you double my measure, you get an acute angle. If you triple my measure, you will get an acute angle again. If you quadruple (four times) my measure, you will get an acute angle yet again! But if you multiply my measure by 5, you will get an obtuse angle measure. What are the possibilities for my measure?

Ans: Let the measure of the angle be denoted as m. According to the conditions, 5 × m is greater than 90°, but 4 × m is less than 90°. This gives the inequality $\frac{90}{5}$ < m < $\frac{90}{4}$.

Thus, m must be greater than 18° but less than 22½°. Based on this, the possible measures for the angle are 19°, 20°, or 21°.

This method of solving inequalities helps in determining specific angle ranges, which is useful in geometric problems that require finding suitable angle measures within a set of conditions. Understanding this approach can be applied in various situations, such as designing objects with specific angular constraints.

Benefits of NCERT Solutions for Class 6 Chapter 2 Lines and Angles Exercise 2.11

• The solutions provide clear and simple instructions to help students measure and classify different types of angles, making the learning process easier.

• By using a protractor, students gain hands-on experience in measuring angles accurately, which is important for geometry.

• The solutions help students understand the differences between acute, obtuse, right, and straight angles, improving their ability to classify angles.

• Real-life examples are included, helping students relate angle concepts to everyday situations and making the topic more engaging.

• The practice problems offer students the chance to apply what they have learned, reinforcing their skills in measuring and classifying angles.

Class 6 Maths Chapter 2: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 2 - Lines and Angles

Conclusion

NCERT Solutions for Class 6 Maths Chapter 2, Exercise 2.11, "Lines and Angles," helps students understand the different types of angles and how to measure them accurately. The clear explanations make it easier to classify angles, such as acute, obtuse, and right angles. Practising these exercises improves student’s skills in measuring and identifying angles, which is important for understanding geometry. With the solutions available as a FREE PDF download, students can study and review at their own pace, making learning both simple and effective.

Chapter-wise NCERT Solutions Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Class 6  Maths 

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.