Students often refer to Kerala State Syllabus SCERT Class 6 Maths Solutions and Class 6 Maths Chapter 1 Angles Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 6 Maths Chapter 1 Solutions Angles
Class 6 Kerala Syllabus Maths Solutions Chapter 1 Angles Questions and Answers
Angles Class 6 Questions and Answers Kerala Syllabus
Drawing Angles (Page 13)
Question 1.
Measure and mark each angle below:
Answer:
(i) 60°
(ii) 135°
(iii) 60°
(iv) 130°
Question 2.
Draw the pictures below in the notebook:
Answer:
(i)
- Draw PQ of length 4 cm.
- From P measure 50° (right measure).
- From Q measure 50° (left).
- Join the two lines.
(ii)
- Make a line of 5 cm.
- From the right end, measure 90° and make a line.
- From the left end, draw a line making a 30° angle.
- Meet the two lines to get the required figure.
(iii)
- Draw a line of length 5 cm.
- From one end, draw a line of 3 cm at an angle of 60°.
- From the other end, draw a line of 3 cm, making 120°.
- Join the angles of the two lines.
(iv)
- Draw a line (dotted) of 6 cm.
- From both ends, draw a line to make a 20° angle on both sides.
- Join the lines together to get the required figure.
Circle Division (Pages 17 & 18)
Question 1.
In each of the pictures below, calculate what fractions of the circle are the yellow and green parts:
Answer:
The measure of an angle inside a circle is 360°
Figure-1
Angle measure of the yellow portion is 20°
Total fractions of the circle is 360° ÷ 20 = 18
The fraction of yellow portion is \(\frac {1}{18}\)
The green portion is \(\frac {17}{18}\)
Figure-2
Angle measure of the yellow portion is 24°
Total fractions of the circle is 360° ÷ 24 = 15
The fraction of yellow portion is \(\frac {1}{15}\)
The green portion is \(\frac {14}{15}\)
Figure-3
Angle measure of the yellow portion is 54°
But for 18° its fraction is, \(\frac {1}{20}\). So for 54° it is \(\frac {3}{20}\).
Therefore the fraction of yellow portion is \(\frac {3}{20}\)
The green portion is \(\frac {17}{20}\)
Figure-4
The angle measure of the yellow portion is 80°
Total fractions of the circle when it is 40°;
360° ÷ 40 = 9. So for 40° it is \(\frac {1}{9}\)
The yellow portion is 80°.
The fraction of yellow portion is \(\frac {2}{9}\)
The green portion is \(\frac {7}{9}\)
Figure-5
Angle measure of the yellow portion is 108°
If it is 36° its fraction is \(\frac {1}{10}\).
That means 36 × 3 = 108
So for 108° it is \(\frac {3}{10}\)
Therefore the fraction of yellow portion is \(\frac {3}{10}\)
The green portion is \(\frac {7}{10}\)
Figure-6
Angle measure of the yellow portion is 150°
If it is 30° its fraction is, \(\frac {1}{12}\).
So for 150° it is \(\frac {5}{12}\).
Therefore the fraction of yellow portion is \(\frac {5}{12}\)
The green portion is \(\frac {7}{12}\)
Question 2.
Mark each of the fractions below as part of a circle and colour the pictures.
(i) \(\frac {3}{8}\)
(ii) \(\frac {2}{5}\)
(iii) \(\frac {4}{9}\)
(iv) \(\frac {5}{12}\)
(v) \(\frac {5}{24}\)
Answer:
(i) \(\frac {3}{8}\)
Angle inside a circle is 360°.
360 is divided into 8 equal parts.
\(\frac {360}{8}\) = 45°
Each part measures 45°.
Angle of shaded region = 3 × 45 = 135°
(ii) \(\frac {2}{5}\)
\(\frac {360}{5}\) = 72°
Each part measures 72°.
Shaded angle = 72 × 2 = 144°
(iii) \(\frac {4}{9}\)
\(\frac {360}{9}\) = 40°
Each part measures 40°.
Shaded angle = 4 × 40° = 160°
(iv) \(\frac {5}{12}\)
\(\frac {360}{12}\) = 30°
Each part measures 30°.
Shaded angle = 30 × 5 = 150°
(v) \(\frac {5}{24}\)
\(\frac {360}{24}\) = 15°
Each part measures 15°.
Shaded angle = 15 × 5 = 75°
Question 3.
Draw the pictures below:
Answer:
Figure-1
Draw a circle and mark 72° in the centre of the circle, and complete the pattern. From the corner-1, draw a line to the corners 3 and 4 similarly, from corner-5 draw a line to the corners 2 and 3, and from corner-2 draw lines to the corners 4 and 5. And colour the picture.
Figure-2
To draw the second figure, make some changes to the above second figure.
Figure-3
Draw an 8-sided figure and draw lines inside the figure to get a square.
Figure-4
Draw it like this.
Class 6 Maths Chapter 1 Kerala Syllabus Angles Questions and Answers
Class 6 Maths Angles Questions and Answers
Question 1.
Draw the angles on the lines that are marked below.
Answer:
Place the point which the bottom line and the perpendicular line joins together in the protractor at the end of the line where the angle should be drawn. For drawing the figures 4 and 5 place the protractor downwards and mark the angles and complete the angles.
Question 2.
Measure and mark each angle below:
Answer:
(i) 50°
(ii) 130°
(iii) 90°
(iv) 105°
(v) 103°
Question 3.
From the angles given below, without measuring it classify them into angles right angle, less than and greater than right angles.
Answer:
Less than right angle: a, d, h
Greater than right angle: b, e, f, g
Right angle: c
Question 4.
Measure the angles below.
Answer:
(a) 120°
(b) 60°
(c) 58°
(d) 125°
(e) 90°
(f) 22°
Question 5.
Divide the circle into 6 equal parts and draw different figures.
Answer:
Question 6.
Draw a picture with 5 and 8 sides.
Answer:
Draw a circle and mark a horizontal line (radius), and mark a 72° angle on it.
Again, mark a 72° angle with each line.
Draw a circle and mark a horizontal line (radius), and mark a 45° angle on it.
Again, mark a 45° angle with each line.
Question 7.
Measure all the angles.
Answer:
(a) 1 – 90°, 2 – 90°, 3 – 130°, 4 – 50°
(b) 1 – 150°, 2 – 120°, 3 – 60°, 4 – 30°
Question 8.
Draw these pictures with the same measurements.
Answer:
Question 9.
Calculate what fraction of the circle is the shaded portion.
Answer:
Figure-1
Angle measure of the shaded portion is 36°
Total fractions of the circle is 360° ÷ 36 = 10
The fraction of shaded portion is \(\frac {1}{10}\)
Figure-2
Angle measure of the shaded portion is 120°
Total fractions of the circle is 360° ÷ 120 = 3
The fraction of shaded portion is \(\frac {1}{3}\)
Class 6 Maths Chapter 1 Notes Kerala Syllabus Angles
→ A figure formed by two lines meeting at a point is called an angle.
→ A protractor is a simple measuring instrument that is used to measure angles.
→ It is in the shape of a semicircle with an inner scale and an outer scale and with markings from 0° to 180° on it.
→ The angle at a square corner is 90°. It is also called a right angle.
→ The measure of a circle is 360°.
An angle is formed when two lines meet at a point. The space between these lines is called an angle. Angles are measured in degrees or radians, and they are grouped based on their size. Angles are very useful in our daily lives. For example, engineers use angles to build houses, bridges, and buildings. Athletes use angles in sports to improve their movements. Carpenters use angles to make things like doors, tables, and chairs. In this chapter, we will learn how to measure angles using a protractor, and how to divide a circle into equal parts.
When Lines Join
Remember how we drew various shapes joining lines straight up and slanted in the section Line Math of the lesson Lines and Circles in the class 5 textbook. Here we draw different patterns using the set square.
If we draw two lines upward of the same length on the two ends of a line and join the top ends using another line, the lengths of the lines in the top and bottom are of the same length.
Instead of drawing the straight-up lines, two slanted lines can be drawn using the set square. We know that the length of the top and bottom lines is are same.
We learn more about the topic straight up and slanted in this unit.
A figure formed by two lines meeting at a point is called an angle.
For example: Arrange these angles based on their size.
Write the numbers of the cones in ascending order.
The angle with less spread out is 4, and the more spread out is 6.
Therefore, the smallest angle is 4 and the largest angle is 6.
Thu,s the arrangement is of the form, 4, 1, 3, 2, 5, 6.
Protractor:
A protractor is a simple measuring instrument that is used to measure angles. It is in the shape of a semicircle with an inner scale and an outer scale, and with markings from 0° to 180° on it.
Considering the inner scale, starting with the bottom line marked 0, there are other lines upward; and as they move up, the angles between them and the bottom line become larger and larger. The numbers at their ends show the sizes of these angles.
How do you measure these angles using a protractor?
Place the protractor at the corner of each angle, as shown below:
Here we can see that the angle on the second figure is 60°.
In the first figure, the slant line of this angle passes between 50 and 60 on the protractor.
We can see that the small lines in the protractor divide the gaps between the multiples of 10 into ten equal parts. Each of them shows a difference of 1°.
Here, in the first figure, the slant line goes through the fifth (slightly larger) line between 50 and 60. That means the angle is 55°.
The angle at a square corner is 90°. It is also called a right angle.
A line making an angle of 90° with another line is said to be perpendicular to the first line.
For example, from the following figures, find out the perpendicular lines.
The lines in Figures 1, 6, and 8 are perpendiculars.
The other figures the angles does not form 90°; therefore, the lines are not perpendicular.
Drawing Angles
Draw an angle of 40° using a protractor.
First, draw a horizontal line. Then place the protractor at its left end as shown below and mark a point at the number 40 in it.
Now remove the protractor and join this point and the left endpoint of the first line to get a 40° angle:
For example: Draw an angle measure of 80°.
First, draw a horizontal line. Then, place the point where the bottom line and the perpendicular line join together in the protractor at the end of the line where the angle should be drawn.
Then mark the point 80° and join this point.
Circle Division
A protractor is a semicircle with 180° measure. Then for a circle, its measure is 360°.
That is, the measure of the angle around the centre of a circle is 360°.
In a circle, 360 equally spaced radii are drawn, and then the angle between any two nearby radii is 1°.
Here, the circle is divided into 360 equal parts.
What if we divide a circle into 4 equal parts?
Its one part is, 360° ÷ 4 = 90°
What if we draw radii 10° apart?
We get 36 radii, which divide the circle into 36 equal parts.
For example, divide a circle into 8 equal parts.
360° ÷ 8 = 45°
Here we get 8 radii, which are 45° apart.
The angle measures of some other portions are;
