You can Download Angles Questions and Answers, Activity, Notes, Kerala Syllabus 6th Standard Maths Solutions Chapter 1 to help you to revise the complete Syllabus and score more marks in your examinations.
Kerala State Syllabus 6th Standard Maths Solutions Chapter 1 Angles
Angles Text Book Questions and Answers
Angles in a circle Textbook Page No. 7
Remember dividing a circle into equal parts using set squares?
(The lesson, Part Number of the class 5 textbook)
See these pictures:
You also know how to divide a circle into equal parts using the corners of the other set square, don’t you?
Look at the angles made at the centre of the circle in each case. If we make the angle larger, does the number of parts increase or decrease?
Answer: If we make the angle larger, the number of parts decreases because the space is getting smaller.
Measure of an angle
We have seen in class 5 how we can divide a circle into three equal parts, using a set square (The section, Three parts, of the lesson, Part Number)
So using the corners of a set square, we can divide a circle into three, four or six parts.
Can we make five equal parts?
Answer: No, we can’t make five equal parts using set square.
Using corners of a set of squares, we cannot make such an angle at the centre.
We need some other method to draw and measure angles of different sizes. Measure lengths of lines starting with small lengths such as millimetres and centimetres.
In the same way, we use a small angle to measure all other angles. This angle is got by dividing a circle into 360 equal parts.
The measure of this angle is said to be 1 degree, and it is written 1°. An angle twice as large as this is said to have measured 2°, thrice as large to have measured 3° and so on.
There is a device in your geometry box to measure angles of different sizes.
It is called a protractor.
See the lines drawn on it?
At the end of each line, we see two numbers, one below the other. Look at the numbers below:
These numbers are the degree measure of the angles made by these lines with the bottom line marked 0.
For example, the angle made by this bottom line and the line just above it is of measure at 10° (10 degrees). The angle made by the bottom line and the line marked 40 is of measure at 40°.
In other words, an angle of 40° is made by 4 angles of 10° each.
Another round of numbers is given on top to draw and measure angles on the left.
How can we measure an angle using a protractor?
Look at this picture.
Note also how the angle is marked.
Answer: It is marked with degrees from 0 to 180 degrees. It can be directly used to measure any angle from 0 to 360 degrees. The markings are made in two ways, 0 to 180 degrees from the right to left and vice versa.
Here are some more examples:
Now draw a line and at one end, thaw a line straight up using the square comer of a set square (The section, Let’s draw of the lesson, When lines Join of the class 5 textbook).
Next, measure this angle using a protractor.
So the angle at a square comer is 90° Such an angle is also called a right angle.
In a figure, we mark a right angle like this:
Without actually measuring the angles below, can you say which are less than 90°, which are more than 90° and which are exactly 90°?
Answer: In the given question, some figures are given.
Now, we will find the figures which are less than 90°, which are more than 90°.
The above figure angle is Less than 90°.
The above figure angle is more than 90°.
The above figure angle is 90°.
The above figure angle is less than 90°.
The above figure angle is 90°.
The above figure angle is more than 90°.
Textbook Page No. 8
Let’s see how we measure an angle in GeoGebra. First mark three points A, B, C. Select the Angle tool and click on B, A, C in this order. (Test what happens if you click in some other order)
We can get the measure of the angle by clicking on the lines AB. AC also.
To get the measure of the angle shown below, in what order should we click?
Answer: To get the measure of the angle by clicking on the lines EF and ED also.
Textbook Page No. 11
Question 1.
Measure all angles below and write names and sizes in degrees below each:
Answer: Given the figures,
Now, we will find the angles and names.
The angle name and size is ∠ABC = 60°.
The below figure angle name and size is ∠EDF= 40°.
The below figure angle name and size is ∠GHI= 110°.
The below figure angle name and size is ∠IKJ= 50°.
The below figure angle name and size is ∠MNO= 115°.
The below figure angle name and size is ∠PQR= 30°.
The below figure angle name and size is ∠YOB= 30°.
The below figure angle name and size is ∠XYZ= 50°, ∠XYT= 20° and ∠TYZ= 30°.
Question 2.
Measure and write all angles of the figure below:
Answer: As given in the question, four figures are given.
Now, we will find the angles of all the angles of figures.
The names of the figures are triangle, square, pentagon and hexagon.
Now, in the triangle, all angles are 60°.
The square all angles are 90°.
In the pentagon, all angles are 108°.
In the Hexagon all angles are 120°.
Drawing an angle
Let’s see how we can draw an angle like this:
Now can you draw this angle?
Answer: As given in the question, the figure is given.
Now, we can draw that given figure step by step.
First, draw a line with the names A and B.
The next step is, to take a protractor. Place the protractor at B point and mark a 40° angle.
Now, take a scale. Draw a line from the 40° angle point marked to B. The line name is marked as C.
The final angle figure is below,
Question 1.
A rectangle has four angles. What is the degree measure of each?
Answer: The degree measure of each angle of a rectangle is 90°.
Question 2.
Draw a rectangle of length 5 centimetres and breadth 3 centimetres using a ruler and a protractor.
Answer: Given the length and breadth are 5cm and 3cm.
Using the protractor with an angle of 90°, we can draw the rectangle.
Below is the rectangle,
Question 3.
Draw the figures shown below with the specified measures, in your notebook:
Answer: Given the figures in the question.
Now, we can draw the given figures in a notebook.
Using Protractor, we can easily draw.
So, the figure is,
(i)
(ii)
(iii)
(iv)
Drawing angles
Draw a line AB in GeoGebra. Select the Angle with the Giving size tool and click on B, and A in this order. In the dialogue box gives the measure of the angle needed and click OK.
We get a new point B’. Join A and B’.
Circle division Textbook Page No. 14
An angle of 1° is got by dividing a circle into 360 equal parts. Putting this the other way round, by drawing 1° degree angles at the centre, we can divide a circle into 360 equal parts.
If we take two of these angles together, we get 2° angles; and 180 equal parts of the circle.
What if take the angles three at a time?
How much would be each angle?
And how many equal parts of the circle?
So, to divide the circle into 30 equal parts, how many of the 360 parts should we take together?
Answer: If we take three of these angles together, we get 3° angles and 120 equal parts of the circle. So, we can divide the circle into 30 equal parts, we get an angle is 12°.
We have divided a circle into equal parts using other corners of set squares. How many equal parts did we get in each case?
360 ÷ 4 = 90
We have divided a circle into equal parts using other corners of set squares. How many equal parts did we get in each case?
Answer: Given the circle,
Now, we can divide the circle into equal parts with each angle.
First, if we divide the circle into 4 equal parts, each angle will be 90°.
If we divide the circle into 6 equal parts, each angle will be 60°.
If we divide the circle into 8 equal parts, each angle will be 45°.
If we divide the circle into 9 equal parts, each angle will be 40°.
Look at this picture:
Using this corner of the set square, we have divided the circle into 8 equal parts.
So, how much is each angle at the centre?
360 ÷ 8 =45
Thus the angle at this corner of the set square is 45°.
In the same way, the angle at the other non-square corner of this set square is also 45°.
Now find the angles at the corners of the other set square.
Now let’s look at our earlier problem of dividing a circle into five equal parts.
To divide a circle into 5 equal parts, what should be the size of the angle at the centre?
360 ÷ 5 = 72
Answer: The size of the angle at the centre is 72°.
Draw angles of 72° at the centre of a circle:
Continuing like this, can’t we divide a circle into five equal parts?
Now can you draw this figure?
What is the name of this figure?
Like this, draw figures of 6, 8, 9, 10, and 12 sides inside a circle.
Answer: Given the figure,
The name of the figure is Pentagon.
(i) The figure of 6 sides inside a circle is below,
The name of the figure is Hexagon.
(ii) The figure of 8 sides inside a circle is below,
The name of the figure is Octagon.
(iii) The figure of 9 sides inside a circle is below,
The name of the figure is Nonagon.
(iv) The figure of 10 sides inside a circle is below,
The name of the figure is Decagon.
(v) The figure of 12 sides inside a circle is below,
Textbook Page No. 17
Question 1.
Can you draw angles of the sizes given below, using a set square? (See the section, Joining angles, of the lesson, When Lines Join, in the class 5 textbook)
(i) 75°
Answer: Given the angle is 75°
We can draw an angle of 30°+45°.
In the figure shown below,
(ii) 105°
Answer: Given the angle is 105°
We can draw angles with 60°+45°.
In the figure shown below,
(iii) 135°
Answer: Given the angle is 135°
We can draw an angle of 90°+45°.
In the figure shown below,
(iv) 15°
Answer: Given the angle is 15°
We can draw an angle of 45°- 30° = 15°
In the figure shown below,
Question 2.
In the figures below, calculate the fraction of the whole circle the green and yellow parts are:
Answer: Given the figures,
Now, we will find the green parts and yellow parts fractions.
(i) In the first figure, the yellow part is 20° and the total circle angle is 360°
So, the yellow part fraction is, 20°/360° = 1/18
The green part fraction is 340°/360° = 17/18
(ii) In the second figure, the yellow part is 24° and the total circle angle is 360°
So, the yellow part fraction is, 24°/360° = 12/180 = 6/90 = 2/30 = 1/15
The green part fraction is 336°/360° = 14/15
(iii) In the third figure, the yellow part is 54° and the total circle angle is 360°
So, the yellow part fraction is, 54°/360° = 3/20
The green part fraction is 306°/360° = 17/20
(iv) In the fourth figure, the yellow part is 80° and the total circle angle is 360°
So, the yellow part fraction is, 80°/360° = 2/9
The green part fraction is 280°/360° = 7/9
(v) In the fifth figure, the yellow part is 108° and the total circle angle is 360°
So, the yellow part fraction is, 108°/360° = 3/10
The green part fraction is 252°/360° = 7/10
(vi) In the sixth figure, the yellow part is 150° and the total circle angle is 360°
So, the yellow part fraction is, 150°/360° = 5/12
The green part fraction is 210°/360° = 7/12
Question 3.
Draw circles and mark the fractional parts given below. Colour them also:
(i) \(\frac{3}{8}\)
Answer: Given the value is \(\frac{3}{8}\)
Now, we will draw the circle and mark the fractional parts.
We know that the total angle of a circle is 360°.
In a given question, the circle total parts are 8.
So, 360°/8 = 45°
Now, we will fill the colour up to 45°.
The circle with colour is as shown below,
(ii) \(\frac{2}{5}\)
Answer: Given the value is \(\frac{2}{5}\)
Now, we will draw the circle and mark the fractional parts.
We know that the total angle of a circle is 360°.
In a given question, the circle total parts are 5.
So, 360°/5 = 72°
Now, we will fill the colour up to 72°.
The circle with colour is as shown below,
(iii) \(\frac{4}{9}\)
Answer: Given the value is \(\frac{4}{9}\)
Now, we will draw the circle and mark the fractional parts.
We know that the total angle of a circle is 360°.
In a given question, the circle total parts are 9.
So, 360°/9 = 40°
Now, we will fill the colour up to 40°.
The circle with colour is as shown below,
(iv) \(\frac{5}{12}\)
Answer: Given the value is \(\frac{5}{12}\)
Now, we will draw the circle and mark the fractional parts.
We know that the total angle of a circle is 360°.
In a given question, the circle total parts are 12.
So, 360°/12 = 30°
Now, we will fill the colour up to 30°.
The circle with colour is as shown below,
(v) \(\frac{5}{24}\)
Answer: Given the value is \(\frac{5}{24}\)
Now, we will draw the circle and mark the fractional parts.
We know that the total angle of a circle is 360°.
In a given question, the circle total parts are 24.
So, 360°/24 = 15°
Now, we will fill the colour up to 15°.
The circle with colour is as shown below,
Angles in a clock
The hands of a clock make different angles at different times: What is the angle between them at 3 o’clock? And at 9 o’clock? The hour hand rotates through 360° in 12 hours. So it rotates through 360° ÷ 12 = 30° in an hour. So at 1 o’clock, the angle between the hands is 30°. What is the angle at 2 o’clock?
And at 4 0’ clock?
Answer: Given the clock figure,
Now, we will find the angle at 2 o’clock and 4 o’clock.
It rotates 30° in an hour. So, the angle between the hands is 30°.
So, the angle at 2 o’clock is 30°+30° = 60°.
Next, the angle at 4 o’clock is 30°+30°+30°+30° = 120°.