Lines And Angles Worksheet

Fill in the blanks Type Questions

1. Genny has eaten an ice cream candy and folded the stick so that the shape of an angle is made. The next day, she does the same thing and makes sure that the angle made is equal to the previous one. 
   
   Now, when she joined the two angles, she realised that the angles are complementary. Then the measure of each angle made by Genny is ___________.
   
   
2. Measures of some angles made between the overhead electric trolley wires are shown below:
   Then, the measure of ∠y is ______________.
   
   
   Multiple Choice Questions
   
   
3. After the renovation, Rohan is shifting his stuff into a separate room. After a while, he lies on the sofa and enjoys a video on the laptop. If a table is placed just near the sofa as shown below, which of the following shapes can you get with the help of a table?
   
   (a)Only line segments
   (b)Line segments and lines
   (c)Angles and line segments
   (d)Lines and angles
   
   
4. A pizza is cut into eight pieces of different sizes. Dhriti picked up any two pieces out of the 8. If the pieces picked up by Dhriti are shown below with the angles mentioned on them, name the type of angles formed.
   
   (a)Vertically opposite angles
   (b)Complementary angles
   (c)Supplementary angles
   (d)Linear pair of angles
   
   
5. Ananya recently started yoga classes, so she asks Poonam to take some photos of her. She finds some humorous and serious pictures of herself when she looks through the photos again. The angles made by the legs in the 1st and 3rd photographs are shown below:
   
   The angles formed by the pair of angles (made by 1st and 3rd photographs) are
   (a)Vertically opposite
   (b)Complementary
   (c)Supplementary
   (d)Linear pair of angles
   
   
6. There are multiple pieces of equipment in a playground. The angles made between the parts of every piece of equipment are shown below:
   
   In which of the following equipment, the pair of angles formed are supplementary?
   (a)Swings and Slide
   (b)Slide and Spinner
   (c)Spinner and Spring Rider
   (d)Climbers and Spring Rider
   
   
7. Shri and Nidhi are having breakfast. Shri is sitting on a chair with a 68° angle formed between her and the breakfast table. How much further backward should Shri lean for the angles to be complementary?
   
   (a)112°
   (b)22°
   (c)52°
   (d)90°
   
   
8. There is an angle created between a roof's two flaps. The resulting angle is then split into two angles, one on the LHS and other on the RHS, as shown, by placing a transparent mirror next to the vertex of the angle.
   
   The mirror and the two flaps so create a pair of ______________ angles.
   (a)Vertically opposite
   (b)Supplementary
   (c)Opposite
   (d)Adjacent
   
   
9. There are three blades in a wind turbine close to Savy’s residence in Pune. Between these blades, the three angles are formed.
   If any two angles are taken into consideration, name the type of angles formed by the resulting pair of angles.
   
   (a)Linear pair of angles
   (b)Supplementary angles
   (c)Complementary angles
   (d)Adjacent angles
   
   
10. Tripti and Ritu take their families on a road trip in their respective vehicles. They arrive at a location with a left and a right turn. Ritu turns in the right direction and Tripti turns in the left direction (on the same road), as shown below:
    
    The pair of angles formed between the roads are
    (a)Linear Pair of angles
    (b)Alternate interior angles
    (c)Complementary angles
    (d)Vertically opposite angles
    
    
11. Rahul bought a land for farming which is 500 metres from his house. He made a boundary around the land with the help of wires and bamboos. Sample of the boundary is shown below:
    
    When looked at the top two wires and the bamboo, there are different angles formed between them.
    Which of the following are vertically opposite angles?
    
    (a)∠a and ∠b
    (b)∠e and ∠g
    (c)∠b and ∠c
    (d)∠f and ∠d
    
    
12. Neeraj went on a school trip with his class and took several pictures illustrating how lines are used in everyday life. The pictures are displayed below:
    
    Which of the following images solely represents intersecting lines?
    (a)A, B, C
    (b)D, E, F
    (c)A, B, E
    (d)C, D, F
    
    
13. Look at the railings at the staircase. The parallel lines and a transversal used in railing makes different angles. If measure of angle x is 75°, find the value of (180° – ∠b).
    
    (a)75°
    (b)105°
    (c)180°
    (d)90°
    
    Subjective Questions
    
    
14. Atharva is just three years old. But he likes to draw something in the book. One day, he randomly draws some figures (shown below) in Rita’s (his sister) drawing book and shows the drawing to her.
    
    Rita then assigns an alphabet to every point visible in the figure. Name the line segments visible in the figure.
    
    
    
15. Ashok assists his mother in drying the washed clothes. He claims that the top angle of the hanger is 100° as he recently learned about angles in class. He then chose the second hanger so that its top angle forms a supplementary angle with the top angle of the first hanger. Find the measure of the second hanger's top angle.
    
    
    
16. Every day at six o'clock, Anchal attends private lessons. Anchal arrives at the tuition in about a minute. While the wall clock is on time, her wristwatch is one minute late. She departs from home at 5:59, but the wall clock reads 6 o'clock. Name the kind of angles created between a clock's three hands by observing the timepiece.
    
    
    
17. Just now, a car drove through a sand desert close to a village. After some time, a bicycle passed by, leaving the tracks left by the wheels of the cycle. Below is a description of the shape the sand took:
    
    Mark all the angles formed and name the vertically opposite angles in the above figure.
    
    
18. A wooden frame (not necessarily rectangular) broke down into pieces. The different corner pieces make different angles. Chetan selects two pieces and join the angles so that the new angles formed is a right angle. If measure of one of the angles is 5 less than 47°, find the measure of other angle.
    
    
19. The branch of a tree is broken due to a storm and so its upper part is touching the ground. There are two angles made between the trunk and branch of a tree. The measure of an angle made between the branch and the lower part of the trunk is three times half of 52 degrees. What could be the measure of the other angle made between the branch and the upper part of the trunk?
    
    
    
20. Aakash and Surya stay in the same society and so share the same rectangular garden. If they walk on the opposite sides of the garden, state whether the paths followed by them are parallel or not.
    
    
21. In a bowling pin game, observe the bowling lanes (track of bowling) and state whether the lanes are parallel or not?
    

Fill in the blanks Type Questions

1. Genny has eaten an ice cream candy and folded the stick so that the shape of an angle is made. The next day, she does the same thing and makes sure that the angle made is equal to the previous one. 
   
   Now, when she joined the two angles, she realised that the angles are complementary. Then the measure of each angle made by Genny is ___________.
   Correct Answer: 45°
   Solution:
   Let the measure of first angle be a°.
   ⇒ a° + a° = 90°
   ⇒ 2a° = 90°
   ⇒ a° = 45°
   So, the measure of each angle made by Genny is 45°
   
   Measures of some angles made between the overhead electric trolley wires are shown below:
2. Then, the measure of ∠y is ______________.
   
   Correct Answer: 80°
   Solution:
   Here, ∠x and an angle with measure 100° are corresponding angles.
   ⇒ ∠x = 100°
   Now, ∠x and ∠y are linear pair of angles.
   ⇒ ∠x + ∠y = 180°
   ⇒ ∠y = 180° – ∠x
   ⇒ ∠y = 180° – 100°
   ⇒ ∠y = 80°
   
   Multiple Choice Questions
   
   
3. After the renovation, Rohan is shifting his stuff into a separate room. After a while, he lies on the sofa and enjoys a video on the laptop. If a table is placed just near the sofa as shown below, which of the following shapes can you get with the help of a table?
   
   (a)Only line segments
   (b)Line segments and lines
   (c)Angles and line segments
   (d)Lines and angles
   Correct Option: (c) Angles and line segments
   Solution:
   
   We can get the following line segments:
   PQ, QR, RS, PS, PT, QU, etc.
   We can also get the following angles:
   ∠PQR, ∠QPS, ∠QRS, ∠RSP, ∠PTU, ∠QUT, etc.
   There are no lines forms in the table.
   Hence, we can get only line segments and angles.
   
   
4. A pizza is cut into eight pieces of different sizes. Dhriti picked up any two pieces out of the 8. If the pieces picked up by Dhriti are shown below with the angles mentioned on them, name the type of angles formed.
   
   (a)Vertically opposite angles
   (b)Complementary angles
   (c)Supplementary angles
   (d)Linear pair of angles
   Correct Option: (b) Complementary angles
   Solution:
   When we add the measures of the two angles formed by the pieces of pizza, we get
   37° + 53° = 90°
   So, the angles are complementary.
   
   
5. Ananya recently started yoga classes, so she asks Poonam to take some photos of her. She finds some humorous and serious pictures of herself when she looks through the photos again. The angles made by the legs in the 1st and 3rd photographs are shown below:
   
   The angles formed by the pair of angles (made by 1st and 3rd photographs) are
   (a)Vertically opposite
   (b)Complementary
   (c)Supplementary
   (d)Linear pair of angles
   Correct Option: (c) Supplementary
   Solution:
   Measure of angle formed in the 1st photograph is 105°.
   Measure of angle formed in the 2nd photograph is 75°.
   Sum of the measures of the angles = 105° + 75° = 180°
   So, the angles are supplementary.
   Thus, the angles formed by the pair of angles (made by 1st and 3rd photographs) are supplementary.
   
   
6. There are multiple pieces of equipment in a playground. The angles made between the parts of every piece of equipment are shown below:
   
   In which of the following equipment, the pair of angles formed are supplementary?
   (a)Swings and Slide
   (b)Slide and Spinner
   (c)Spinner and Spring Rider
   (d)Climbers and Spring Rider
   Correct Option: (b) Slide and Spinner
   Solution:
   For two angles to be supplementary, their sum has to be 180°.
   70° + 70° = 140° ≠ 180°
   125° + 55° = 180°
   85° + 95° = 180°
   123° + 70° = 193° ≠ 180°
   146° + 104° = 250° ≠ 180°
   So, the pair of angles in the slide and spinner are supplementary.
   
   
7. Shri and Nidhi are having breakfast. Shri is sitting on a chair with a 68° angle formed between her and the breakfast table. How much further backward should Shri lean for the angles to be complementary?
   
   (a)112°
   (b)22°
   (c)52°
   (d)90°
   Correct Option: (b) 22°
   Solution:
   Let Shri leans backward by x°.
   Since, the angles need to be complementary.
   ⇒ 68° + x° = 90°
   ⇒ x° = 22°
   So, Shri should lean backward by 22°.
   
   
8. There is an angle created between a roof's two flaps. The resulting angle is then split into two angles, one on the LHS and other on the RHS, as shown, by placing a transparent mirror next to the vertex of the angle.
   
   The mirror and the two flaps so create a pair of ______________ angles.
   (a)Vertically opposite
   (b)Supplementary
   (c)Opposite
   (d)Adjacent
   Correct Option: (d) Adjacent
   Solution:
   The two angles are adjacent to each other.
   So, the pair of angles formed by the mirror and the two flaps are adjacent angles.
   
   
9. There are three blades in a wind turbine close to Savy’s residence in Pune. Between these blades, the three angles are formed.
   If any two angles are taken into consideration, name the type of angles formed by the resulting pair of angles.
   
   (a)Linear pair of angles
   (b)Supplementary angles
   (c)Complementary angles
   (d)Adjacent angles
   Correct Option: (d) Adjacent angles
   Solution:
   When we take any two angles say A and B or B and C or C and A, they are adjacent to each other.
   So, the pair of angles formed are adjacent angles.
   
   
10. Tripti and Ritu take their families on a road trip in their respective vehicles. They arrive at a location with a left and a right turn. Ritu turns in the right direction and Tripti turns in the left direction (on the same road), as shown below:
    
    The pair of angles formed between the roads are
    (a)Linear Pair of angles
    (b)Alternate interior angles
    (c)Complementary angles
    (d)Vertically opposite angles
    Correct Option: (a) Linear Pair of angles
    Solution:
    The left and right roads together form a straight line.
     
    Sum of the angles formed between the roads is 180°.
    So, the angles formed between the three ways are linear pair of angles.
    
    
11. Rahul bought a land for farming which is 500 metres from his house. He made a boundary around the land with the help of wires and bamboos. Sample of the boundary is shown below:
    
    When looked at the top two wires and the bamboo, there are different angles formed between them.
    Which of the following are vertically opposite angles?
    
    (a)∠a and ∠b
    (b)∠e and ∠g
    (c)∠b and ∠c
    (d)∠f and ∠d
    Correct Option: (b) ∠e and ∠g
    Solution:
    The pair of vertically opposite angles are:
    ∠a and ∠c
    ∠b and ∠d
    ∠e and ∠g
    ∠f and ∠h
    
    
12. Neeraj went on a school trip with his class and took several pictures illustrating how lines are used in everyday life. The pictures are displayed below:
    
    Which of the following images solely represents intersecting lines?
    (a)A, B, C
    (b)D, E, F
    (c)A, B, E
    (d)C, D, F
    Correct Option: (c) A, B, E
    Solution:
    Pictures A, B and E represents intersecting lines only.
    Pictures C and F represents parallel lines only.
    Picture D represents parallel and intersecting lines both.
    
    
13. Look at the railings at the staircase. The parallel lines and a transversal used in railing makes different angles. If measure of angle x is 75°, find the value of (180° – ∠b).
    
    (a)75°
    (b)105°
    (c)180°
    (d)90°
    Correct Option: (a) 75°
    Solution:
    Here, lines l and m are parallel and line n is a transversal.
    ∠x and ∠a are corresponding angles
    ⇒ ∠x = ∠a
    ⇒ ∠a = 75°
    Now, ∠a and ∠b are linear pair of angles.
    ⇒ ∠a + ∠b = 180°
    ⇒ ∠b = 180° – ∠a
    ⇒ ∠b = 180° – 75°
    ⇒ ∠b = 105°
    ⇒ 180° – ∠b = 180° – 105° = 75°
    
    Subjective Questions
    
    
14. Atharva is just three years old. But he likes to draw something in the book. One day, he randomly draws some figures (shown below) in Rita’s (his sister) drawing book and shows the drawing to her.
    
    Rita then assigns an alphabet to every point visible in the figure. Name the line segments visible in the figure.
    
    Solution:
    Line segments visible in the figure are:
    AB, BC, DE, EF and HI
    
    
15. Ashok assists his mother in drying the washed clothes. He claims that the top angle of the hanger is 100° as he recently learned about angles in class. He then chose the second hanger so that its top angle forms a supplementary angle with the top angle of the first hanger. Find the measure of the second hanger's top angle.
    
    Solution:
    For a pair of angles to be supplementary, their sum has to be 180°.
    Measure of one of the angles is 100°.
    Let the measure of the second hanger's top angle be a°.
    ⇒ 100° + a° = 180°
    ⇒ a° = 80°
    Thus, the measure of the second hanger's top angle will be 80°.
    
    
16. Every day at six o'clock, Anchal attends private lessons. Anchal arrives at the tuition in about a minute. While the wall clock is on time, her wristwatch is one minute late. She departs from home at 5:59, but the wall clock reads 6 o'clock. Name the kind of angles created between a clock's three hands by observing the timepiece.
    
    Solution:
    At 6 ‘O’ clock, the hour hand and minute hand are straight in the opposite directions.
    The seconds’ hand will be somewhere between them.
    So, an angle of 180° is made between the hour hand and minute hand.
     
    ⇒ ∠a + ∠b = 180°
    Thus, the three hands of a clock make linear pair of angles.
    
    
17. Just now, a car drove through a sand desert close to a village. After some time, a bicycle passed by, leaving the tracks left by the wheels of the cycle. Below is a description of the shape the sand took:
    
    Mark all the angles formed and name the vertically opposite angles in the above figure.
    Solution:
    The angles formed in the given shape are as follows:
    
    The pair of vertically opposite angles are:
    ∠a and ∠c
    ∠b and ∠d
    ∠e and ∠g
    ∠f and ∠h
    
    
18. A wooden frame (not necessarily rectangular) broke down into pieces. The different corner pieces make different angles. Chetan selects two pieces and join the angles so that the new angles formed is a right angle. If measure of one of the angles is 5 less than 47°, find the measure of other angle.
    Solution:
    As joining the angles results into a right angle.
    So, the angles are complementary.
    Measure of one of the angle = (47 – 5)° = 42°
    Measure of another angle = 90° – 42° = 48°
    
    
19. The branch of a tree is broken due to a storm and so its upper part is touching the ground. There are two angles made between the trunk and branch of a tree. The measure of an angle made between the branch and the lower part of the trunk is three times half of 52 degrees. What could be the measure of the other angle made between the branch and the upper part of the trunk?
    
    Solution:
    As the branch of a tree is broken but it is still in contact with the stem, so the angles formed between the branch and the trunk are in linear pair.
    Measure of one of the angles = 3 × (½ × 52)° = 3 × 26° = 78°
    Measure of another angle = 180° – 78° = 102°
    Measure of the angle made between the branch and the upper part of the trunk is 102°.
    
    
20. Aakash and Surya stay in the same society and so share the same rectangular garden. If they walk on the opposite sides of the garden, state whether the paths followed by them are parallel or not.
    Solution:
    The opposite sides of a rectangle are always parallel.
    Now, as Aakash and Surya walk on the opposite sides of the garden.
    So, the paths formed are parallel.
    Thus, they are walking on parallel lines.
    
    
21. In a bowling pin game, observe the bowling lanes (track of bowling) and state whether the lanes are parallel or not?
    
    Solution:
    The tracks of bowling here are parallel and they are made parallel as each track is made from a rectangular piece of wood.