NCERT Solutions Class 6 Maths Chapter 2 Lines and Angles Exercise 2.9

NCERT Solutions Class 6 Maths Chapter 2 "Lines and Angles" Exercise 2.9 generally represents an important moment in students' journey to learning the basics of geometry; in this case, one important aspect of geometry is introduced to students with Exercise 2.9, measuring angles.  

In NCERT Solutions Class 6 Maths Chapter 2 Lines and Angles Exercise 2.9, students apply concepts like adjacent angles, vertically opposite angles, and angles on a straight line to solve practical geometry questions. These problems enhance spatial understanding and logical thinking. 

1.0Download NCERT Solutions of Class 6 Maths Chapter 2 Lines and Angles Exercise 2.9

Have you downloaded easily-written solutions to all of the questions in this exercise, Exercise 2.9 These step-by-step NCERT Solutions will help you learn angle properties so you will be able to solve geometry questions and problems reliably and efficiently.

2.0Key Concepts of Exercise 2.9

• Engagement with the protractor: Familiarization of the parts of a protractor (baseline, center point, inner and outer scale) and how to use them to measure angles.
• Measuring angles: Learning the correct procedure to place the center of the protractor on the vertex of the angle and the baseline along one of the angle's arms; then reading the angle measure in degrees.
• Constructing angles: Learning how to use a protractor to draw angles of particular measures from a given ray.
• Reading scales: Learning how to discern between the inner and outer scales and when to use each scale, based on the direction in which the angle opens.
• Estimating angle measures: Having the ability to estimate angle measures before reaching for a protractor will allow students to check that their estimate was correct.
• Understanding degree as a unit: Reinforcing students' understanding that degree is the standard unit of measurement for angles.

3.0NCERT Exercise Solutions Class 6 Chapter 2 Lines and Angles : All Exercises 

Find all the NCERT Exercises Solutions from class 6 Maths Chapter 2:

4.0NCERT Class 6 Maths Chapter 2 Exercise 2.9 : Detailed Solutions

1. Write the measures of the following angles:

(a) ∠KAL,

Notice that the vertex of this angle coincides with the centre of the protractor. So the number of units of 1 degree angle between KA and AL gives the measure of ∠KAL. By counting, we get ∠KAL=30∘.

Making use of the medium sized and large sized marks, is it possible to count the number of units in 5 s or 10 s ?

(b) ∠ WAL

(c) ∠TAK

Sol. (a) ∠KAL=3×10∘=30∘

(b) ∠WAL=5×10∘=50∘

(c) ∠TAK=12×10∘=120∘

2. Find the degree measures of the following angles using your protractor.

Sol.

(a) ∠IHJ=47∘

(b) ∠IHJ=24∘

(c) ∠IHJ=110∘

3. Find the degree measures of different angles in your classroom using your protractor.

Sol. Angle formed at corner of blackboard =90∘, Angle formed at corner of desk =90∘

4. Find the degree measures for the angles given below. Check if your paper protractor can be used here!

Sol. (a) ∠IHJ=42∘

(b) ∠IHJ=116∘

5. How can you find the degree measure of the angle given below using a protractor?

Sol. We can measure ∠1=100∘ using protractor and subtract it from 360∘ to find the the measure 

6. Measure and write the degree measures for each of the following angles:

Sol.

(a) Measure of given angle is 80∘

(b) Measure of given angle is 120∘

(c) Measure of given angle is 60∘

(d) Measure of given angle is 130∘

(e) Measure of given angle is 128∘

(f) Measure of given angle is 61∘

7. Find the degree measures of ∠BXE,∠CXE,∠AXB and ∠BXC.

Sol.

(a) ∠BXE=115∘

(b) ∠CXE=85∘

(c) ∠AXB=65∘

(d) ∠BXC=30∘

8. Find the degree measures of ∠PQR,∠PQS and ∠PQT.

Sol.

(a) ∠PQR=45∘

(b) ∠PQS=100∘

(c) ∠PQT=150∘

9. Make the paper craft as per the given instructions. Then, unfold and open the paper fully. Draw lines on the creases made and measure the angles formed.

Sol. Do it yourself

10. Measure all three angles of the triangle shown in Fig. 2.21 (a), and write the measures down near the respective angles. Now add up the three measures. What do you get? Do the same for the triangles in Fig. 2.21 (b) and (c). Try it for other triangles as well, and then make a conjecture for what happens in general! We will come back to why this happens in a later year.

Sol.

In general, we observe that sum of all angles of a triangle is 180∘.

(Where are the angles?)

11. Angles in a clock:

a. The hands of a clock make different angles at different times. At 1 o'clock, the angle between the hands is 30∘. Why?

b. What will be the angle at 2 o'clock? And at 4 o'clock? 6 o'clock?

c. Explore other angles made by the hands of a clock.

Sol.

a. There are 12 numbers on a clock representing 12 hours. The total angle covered in 12 hours is 360∘.

So, the angle between two successive numbers =12360∘​=30∘

That is why at 1o′ clock, the angle between the hands is 30∘.

b. The angle at 2′ o'clock =2×30∘=60∘

The angle at 4′ clock =4×30∘=120∘

The angle at 6∘ clock =6×30∘=180∘

c. The other angle made by hands

12. The angle of a door: Is it possible to express the amount by which a door is opened using an angle? What will be the vertex of the angle and what will be the arms of the angle?

Sol. Yes, It is Possible.

Here, vertex is B and arms are BA and BC .

13. Vidya is enjoying her time on the swing. She notices that the greater the angle with which she starts the swinging, the greater is the speed she achieves on her swing. But where is the angle? Are you able to see any angle?

Sol. Yes, an angle can be seen.

14. Here is a toy with slanting slabs attached to its sides; the greater the angles or slopes of the slabs, the faster the balls roll. Can angles be used to describe the slopes of the slabs? What are the arms of each angle? Which arm is visible and which is not?

Sol. Yes, angles can be used to describe the slope of the slabs.

Greater the angle, Greater the slope.

For Each angle one arm is a side and one arm is the slope.

The vertical arm is not visible whereas the other arm is visible.

15. Observe the images below where there is an insect and its rotated version. Can angles be used to describe the amount of rotation? How? What will be the arms of the angle and the vertex?

Hint: Observe the horizontal line touching the insects.

Sol. Observe the vertical and horizontal lines touching the insects. The rotation from vertical to horizontal position makes an angle. We can imagine the meeting point of the two lines as the vertex, and these two lines as arms of the angle as shown in the picture.

Fig (ii)

In the figure (i) given above, the insect is rotated through an angle of 90∘ in the clockwise direction and in the figure (ii), the insect is rotated through an angle of 90∘ in the anticlockwise direction.

5.0Key Features and Benefits Class 6 Maths Chapter 2 Lines and Angles: Exercise 2.9

• Build confidence and master angle-related problems. 
• Enhance their understanding of geometric concepts through application.
• To develop logical and analytical thinking skills.
• To have clear, step-by-step solutions to complex questions.
• To develop an understanding and be prepared for higher topics in higher classes and prior to their exams.