Students often refer to Kerala State Syllabus SCERT Class 6 Maths Solutions and Class 6 Maths Chapter 9 Lines and Angles Questions and Answers Notes Pdf to clear their doubts.
SCERT Class 6 Maths Chapter 9 Solutions Lines and Angles
Class 6 Kerala Syllabus Maths Solutions Chapter 9 Lines and Angles Questions and Answers
Lines and Angles Class 6 Questions and Answers Kerala Syllabus
When Lines Meet
In-text Questions (Page Number 130)
Question 1.
Some pictures of two lines that meet are shown below. The measure of one of the two angles made on either side is also given. Find the measure of the other angle:
Answer:
1. 100° – 80°
2. 45° – 135°
3. 30° – 150°
4. 80° – 100°
From this, we can understand that a line drawn from another line, or two Lines meet, the sum of the angles made thus will be 180°.
The sum of the two angles made when two lines meet is 180°.
Question 2.
From the following figure, what is the measurement of the third angle?
Answer:
Since the sum of three angles is 180°.
Here, the sum of two angles is 85° + 150 = 100°
Therefore, the third angle is 180° – 100 = 80°
Question 3.
Now look at the angles in the following figure.
Answer:
Sum of the three angles = 70° + 20° + 40° = 130°
So the fourth angle is 180° – 130° = 50°
When Lines Meet (Page Numbers 131-132)
Question 1.
In the picture below, what is the angle on the left?
Answer:
The sum of two angles = 50° + 25° = 15°
The third angle = 180° – 15° = 105°
Question 2.
In the picture below, what is the measure of the angle between the lines?
Answer:
Let’s check the corners of the set-squares.
From the corners which are joined, one is 45°, and the other is 60°.
So, adding these two angles, we get 60° + 45° = 105°
Therefore the middle angle = 180° – 105° = 75°
Question 3.
Among the three angles marked in the picture below, the angles on the left and right are equal. How much is each?
Answer:
As one angle is 30°, the sum of the angles of the other two angles will be 180° – 30° = 150°
Since those two angles are equal, one angle will be \(\frac {150}{2}\) = 75°
Question 4.
Of the two angles made when two lines meet, one angle is double the other. What are the measures of the two angles?
Answer:
We need to find two numbers whose sum is 180, and one number is double the other.
If those numbers are the same, then they are 90° each.
If we subtract 30° from one and add 30° from the other, we get
90° – 30° = 60°
90° + 30° = 120°
When they are added together, we get 180°.
When Lines Intersect (Page Number 134)
Question 1.
The pictures below show various pairs of intersecting lines. One of the four angles thus made is given in each picture. Calculate the other three angles and mark them in each picture:
Answer:
1. 45°, 135°, 45°, 135°
2. 120°, 60°, 120°, 60°
3. 90° each
(Page Number 136-137)
Question 1.
In the four angles made by two intersecting lines, the sum of the two angles is 100°. Calculate all four angles.
Answer:
As the sum of two angles is 100, they are opposite angles (if they are adjacent angles, their sum is 180).
As the opposite angles are equal, each of them is 50°. So one of its adjacent angles is 130°.
So the pair of adjacent angles of another angle is also 130°.
So the measurement of four angles is 50°, 130°, 50°, 130°.
Question 2.
In the four angles made by two intersecting lines, one angle is half of another. Calculate all four angles.
Answer:
Since one angle is half of another, the two angles must be adjacent (otherwise, vertically opposite angles would be equal).
The sum of adjacent angles on a straight line is 180°.
Given that one angle is half of the other, the angles must be 120° and 60°.
Therefore, the vertically opposite angles are also 120° and 60°.
So, the four angles are 120°, 60°, 120°, and 60°.
Question 3.
The two pictures below show lines passing through a point. The measures of some of the angles are given in each. Calculate the other marked angles in each:
Answer:
Non Intersecting Lines & Line and Slant (Page Number 144)
Question 1.
Find the pairs of parallel lines in the picture below and write them down:
Answer:
Similar pairs
1. A, F (F is 70° and the other angle is 110°)
2. B, D (F is 100° and the other angle is 80°)
3. C, E (Both are perpendicular)
Parallelograms (Page Number 146)
Question 1.
Draw the parallelograms shown below:
Answer:
1. Draw a line of 4 cm.
Draw angles of 70° and 110° on each side.
Mark a point at 3cm on each of these lines.
Join these points with a line.
2. Draw a line of 5 cm.
Draw an angle of 60° from the left side and 120° on the right side.
Mark a point at 3cm on each of these lines.
Join these points with a line.
3. Draw a line of 4 cm.
Draw an angle of 50° from the left side and 130° on the right side.
Mark a point at 2cm on each of these lines.
Join these points with a line.
4. Draw a line of 3 cm.
Draw an angle of 40° from the left side and 140° on the right side.
Mark a point at 3cm on each of these lines.
Join these points with a line.
This is a parallelogram with equal sides.
Class 6 Maths Chapter 9 Kerala Syllabus Lines and Angles Questions and Answers
Class 6 Maths Lines and Angles Questions and Answers
Question 1.
In each of the following figure give the angle marked as ‘?’
Answer:
(a) 140°
(b) 50°
(c) 60°
Question 2.
Write all the angles in the picture given.
Answer:
(a) (a) 60°, (b) 120°, (c) 60°
(b) (a) 50°, (b) 130°, (c) 50°
(c) (a) 70°, (b) 40°, (c) 70°, (d) 70°
(d) (a) 60°, (b) 30°, (c) 90°, (d) 60°
Question 3.
When two angles intersect each other to make an angle of 90°, what will be the other angles?
Answer:
90° each
Question 4.
In the figure, one angle is a right angle and the other two are equal.
Answer:
Angle 1 = 45°
Angle 2 = 45°
Question 5.
In the figure given, which of the angles are the same? Which of the angle having sum of 180°?
Answer:
Equal angles are a and c; b and d
Having sum 180° = a and b; c and d; a and d; b and c.
Question 6.
Draw a line of 8 cm and draw a parallel line of it at a distance of 3 cm.
Answer:
Draw a line of 8 cm. Place a scale perpendicularly and set a square on the line.
Mark a point 3cm away from the line.
Move the set square to the point marked and draw a line along the point.
Question 7.
Draw a line and draw another line having an angle of 70°. Draw a parallel line with the second line.
Answer:
Draw a line a mark a point.
Draw an angle of 70° from this point.
Similarly, mark a point on the left side.
Draw an angle of 70° from this point.
Question 8.
Draw a parallelogram of 6 cm and another side of 4 cm and having an angle of 45°.
Answer:
Draw a line of 6 cm.
Draw an angle of 45° on one side and 135° on another side.
Mark a point on 4 cm of each line.
Join the points with a line.
Question 9.
In this picture, which of them are opposite angles?
Answer:
1 and 3
2 and 4
If angle 1 is 110°, then angle 3 is also 110°.
Then the angle 2 is 70°, so angle 4 is also 70°.
In the four angles made by two intersecting lines,
- The sum of each pair of adjacent angles is 180°.
- Each pair of opposite angles is equal.
Question 10.
Look at the angles given in the picture. Which are adjacent angles and which are opposite angles?
If angle a = 100°, find the measurement of the other angles.
Answer:
Adjacent angles: a, b; b, c; c, d; a, d
Opposite angles: a, c; b, d
Angle a = 100°
Angle b = 80°
Angle c = 100°
Angle d = 80°
Question 11.
Which are equal pairs in the given figure? Which pairs have a sum of 180°?
Answer:
Equal pairs: 1 and 3; 2 and 4
Pairs having a sum of 180°:
- 1 and 2
- 2 and 3
- 3 and 4
- 1 and 4
Question 12.
From the following, find which of them are parallel lines?
Answer:
1. 2, 9
2. 3, 6
3. 4, 7
4. 5, 8
Question 13.
Draw the picture given below in your notebook, and draw parallel lines to the slanted lines.
Answer:
Question 14.
In the following figures, there is a measurement of one angle. Find the other angles without measuring.
Answer:
(A) 140°, 40°, 140°
(B) Each 90°
(C) 100°, 80°, 100°
Class 6 Maths Chapter 9 Notes Kerala Syllabus Lines and Angles
→ The sum of the two angles made when two lines meet is 180°
→ When two lines intersect, four angles are formed. If the lines are perpendicular to each other, all four are 90°.
→ If the lines are slanted, there are two small angles and two large angles; in these,
- Both the smaller angles have the same measure.
- Both the larger angles have the same measure.
- The sum of a small angle and a large angle is 180°.
→ In the four angles made by two intersecting lines,
- The sum of each pair of adjacent angles is 180°
- Each pair of opposite angles is equal
→ Lines that keep the same distance apart and will never meet are called parallel lines.
→ A quadrilateral with each pair of opposite sides parallel is called a parallelogram.
→ Any four-sided figure is called a quadrilateral.
In this chapter, we learn more about the lines and the shapes that are made by lines and angles. When these lines intersect, we get different shapes. We also learn about the lines that do not intersect and their peculiarities.
When Lines Meet
You have learned how to draw angles and measure them. Try to measure them.
How many degrees are they each?
A = ___________
B = ___________
C = ___________
D = ___________
Look at the angles given below.
The first angle is 90°, which is a right-angle triangle. In this type of angles two lines are always vertical.
The second angle is less than the right angle, which means its angle is less than 90°.
In this type angles the second line slants inside.
The third angle is greater than the right angle, which means its angle is greater than 90°.
In this type angles the second line slants outwards.
Now, let’s check some other points regarding angles.
We know that the angles are made by drawing a line and then drawing another line from one of its ends.
These types of angles are of three types.
1. If we draw a line and the second line is drawn straight up, we get a right angle.
2. Now, what if the second line is drawn slanted towards the left side?
The angle on the left side becomes smaller than 90°, and the angle on the right side becomes larger than 90°.
The amount by which the angle on the left side is less than 90° is the same amount by which the angle on the right side is greater than 90°.
That is, the sum of those two angles is 180°.
3. Now, what if the second line is drawn slanted towards the right side?
The angle on the right side becomes smaller than 90°, and the angle on the left side becomes larger than 90°.
The amount by which the angle on the right side is less than 90° is the same amount by which the angle on the left side is greater than 90°.
That is, the sum of those two angles is 180°.
So, in these types of angles, if we know one angle, we can find the other.
Look at the picture.
Since the smaller angle is 50°, the other angle will be 130°. Because when the two angles are added, their sum is 180°.
That means the smaller angle is 40° less than 90° and the bigger angle is 40° greater than 90°.
One angle is given; find the other one of the following angles.
Answer:
- 160°
- 90°
- 120°
- 145°
- 20°
- 50°
When Lines Intersect
Now let’s check the peculiarities of the angles formed by the lines that intersect.
When a line intersects another line, four angles are formed.
In this, if we add the first and second angle we get 180°.
Like this, which of the pairs of angles will have a sum of 180°?
- 2 & 3
- 3 & 4
- 1 & 4
Let’s check the same thing with the measurement of angles.
Here, if one angle is 120°, then the adjacent angle will be 60°.
Like this, in these types of angles, two angles will have the same measurements.
Then what will be the measurements of the other angles of the following figure?
The angle on the right side of 30° is 150°.
The opposite angle of 30° is also 30°, and the bottom of 30° is 150°.
What if the line intersecting is straight downwards?
Then all the angles formed here will be 90°. So in general,
When two lines intersect, four angles are formed. If the lines are perpendicular to each other. All four are 90° angles.
If the lines are slanted, there are two small angles and two large angles; in these,
- Both the smaller angles have the same measure
- Both the larger angles have the same measure
- The sum of a small angle and a large angle is 180°
Angles that are next to each other are called adjacent angles. When two lines intersect, they form four angles, which can be paired in different ways.
Some of these pairs have the same measure. In each such pair, the angles are next to each other.
Look at the picture given below.
When two lines intersect like this, we can find one thing from this. One angle and its opposite angle are always the same.
Non-Intersecting Lines
These lines won’t meet however much we extend them, in any direction, because the distance between them is equal everywhere.
Lines like these, which keep the same distance apart and will never meet, are called parallel lines.
To draw a line parallel to another line, first draw a line.
Then draw perpendicular lines of equal length from both ends of the line, and join the endpoints of these perpendicular lines.
This new line will be parallel to the original line.
Look at this picture. Draw a line first.
Then, draw two perpendicular lines from both ends of the line using set squares or use a protractor to draw 90 ° angles.
Now mark the same distance on both the perpendicular lines.
Join the points marked on both the perpendicular lines.
To avoid lots of unwanted lines for drawing a neat parallel line like this, we can use setsquares and a scale.
First, draw a line. Now, place a scale perpendicular to the line firmly. Place a set square close to the line and scale.
Now move the set square by placing the scale firmly and draw a line above the line from the tip of the set square.
Now, if we draw a line, and we want to draw a parallel line that is 4 cm away from this line.
Draw a line first. Place a scale perpendicular to this line firmly and place a setsquare on the line which is close to the scale.
Now move the set square in the upward direction till the measurement reaches 4cm on the scale.
Now remove the scale and draw the line starting from the tip of the setsquare.
Now, what if we draw lots of perpendicular lines in a line?
None of these perpendicular line won’t meet if this extended.
Now we can understand that any perpendicular lines drawn in a line are parallel lines.
Line and Slant
Now draw a line that is perpendicular to and slanted to a line. The lines drawn now are not parallel.
We need to draw a line that is not perpendicular, but a line that is parallel to the line.
A line is drawn 60° slanted from a line. If we want to draw a line parallel to this line, we should draw another line with the same slant.
Since two lines have the same slant, they are parallel to each other.
From this we can understand that the lines which having same slant in a line are parallel to each other.
Method of Drawing
Draw a line and make an angle in a place. Draw another angle in some other place.
Now draw this picture in your notebook.
Draw a parallel line for the slanted line.
Since the angle of the slanted line is 80°, draw a line from a certain distance from this line, which has an angle of 80°, and they will be parallel to each other.
The angle on the right side is 100°, since the adjacent pair is 80° (since they are adjacent angles, and their sum will be 180°).
Parallelograms
Any four-sided figure is called a quadrilateral.
The following figures are quadrilaterals.
All of them have four sides.
1. Opposite sides are equal; it is a rectangle
2. All sides are equal; it is a square
Look at the 5th figure.
Their opposite sides are equal and parallel.
Since their corners are not straight, they are not a rectangle.
A quadrilateral with each pair of opposite sides parallel is called a parallelogram.
If two parallel lines are drawn as shown in this figure, we get a parallelogram.
We can draw a parallelogram using a protractor.
- Draw a line of 5 cm.
- Draw an angle of 50° on the left side.
- Mark a point on 3cm of this line.
- Draw an angle of 130° on the other end of the bottom line.
- Mark a point on 3cm of this line.
- Join the two points on these lines.
By changing the length of the sides and angles, we can draw this in different ways.
Draw 90° angles in between the sides and check what we get?
Answer:
Now the angles are straight and parallel, we call this a rectangle.