Class 5 Mathematics · Chapter 3

3. Angles as Turns

Solutions to all Let Us Do, Let Us Think and Fun with Turns questions. CBSE / NCERT Class 5 Maths Mela.

Introduction

1Can you recognise the child in the picture who has made a full turn? Who has made a half turn? How do you know?

At the start, all four children face the front.

After “Statue!”, B faces the front again. So, B has made a full turn.

A faces the back (the opposite side). So, A has made a half turn.

D faces sideways. D has made a quarter turn.

2Give examples of real-life situations where you observe turns.

Opening a door, turning a tap, turning a key, the hands of a clock, a ceiling fan, a giant wheel and a steering wheel.

3Reema takes turns in the same direction. Fill in the blanks.

Two half turns are like a full turn.

Two quarter turns are like a half turn.

Four quarter turns are like a full turn.

4Write some of the everyday objects that involve turns.

Taps, doors, keys, bottle lids, fans, clock hands and steering wheels.

5What is the maximum possible turn in each of these cases? Check and tick.

Object	Less than a 14 turn	More than a 14 turn
Clothes clip	✓
Door with hinge		✓
Tongs	✓
Scissors	✓
File cover		✓

Objects that make a half turn: door with hinge, file cover.

Objects that make a full turn: none of these. (A file cover can be folded back almost a full turn.)

Let Us Do

(a)Making a paper fan. Use your paper fan to show different acute angles and obtuse angles.

Activity. Open the fan a little to show an acute angle. Open it more than a quarter turn but less than a half turn to show an obtuse angle.

1Can the two acute turns together make another acute turn?

Sometimes yes, sometimes no.

Two small acute turns can make an acute turn. For example, 112 + 112 = 16 turn.

Two bigger acute turns can make a right or obtuse angle. For example, 18 + 18 = 14 turn (right angle).

(b)Look at the angles marked in the house. Write your answers as right, acute or obtuse angle.

A: Obtuse angle
B: Right angle

C: Acute angle
D: Acute angle

E: Acute angle
F: Right angle

G: Right angle
H: Obtuse angle

(c)Make a 5-sided shape with 2 right angles, 2 obtuse angles, and 1 acute angle in your notebook.

Draw a house shape with a tall, pointed roof.

The two bottom corners are right angles. The top corner of the roof is pointed, so it is acute. The two corners where the roof meets the walls are obtuse.

Check: the shape has 5 sides and 5 corners — 2 right, 2 obtuse and 1 acute.

(d)Look at the angle formation between the legs of these gymnasts. Identify whether the angles are acute, obtuse, right or straight.

Acute angle
Right angle
Obtuse angle
Obtuse angle
Straight angle

Angle Measuring Tool

1What angle have you made with a 28 turn? What angle have you made with a 48 turn?

A 28 turn = 14 turn. It makes a right angle.

A 48 turn = 12 turn. It makes a straight angle.

A 68 turn completes a 34 turn. An 88 turn completes a full turn.

Let Us Think

1In the circles, the end points of 12, 14 and 18 turns are shown. Draw arrows to show the starting points.

12 turn: Draw the starting arrow exactly opposite to the end arrow. For the arrow pointing down-right, start at up-left. For the arrow pointing up-right, start at down-left.

18 turn (clockwise): Go back by half of a quarter. For the arrow pointing right, start at up-right. For the arrow pointing down-right, start at the right.

14 turn (clockwise): Go back by a quarter. For the arrow pointing up-left, start at down-left. For the arrow pointing down, start at the right.

If the turn is taken anti-clockwise, draw the starting arrow on the other side by the same amount.

2Can you guess what turn of the straw will be equal to half of a 16 turn?

Half of a 16 turn = 112 turn.

Let Us Do

1Guess the measures of each of the angles shown below. Then, check using your angle measuring tools. State whether each angle is acute, right, or obtuse.

Reading the angles from left to right, top row first:

Top-left angle: about 112 turn — acute
Angle with one vertical arm: 18 turn — acute
Angle in the top middle: about 16 turn — acute
Top-right angle: 14 + 112 = 412 turn — obtuse
Bottom-left angle (on the flat line): 16 turn — acute
Bottom middle angle: 14 turn — right angle
Bottom-right angle: 14 + 18 = 38 turn — obtuse

2Guess the measure of the turns made by the arrow in each of the following cases.

(a) 14 + 18 turn or 38 turn (given)

(b) 12 + 18 turn or 58 turn

(d) About 14 + 16 turn or 512 turn (a little less than a half turn)

3Measure each angle in the given shapes. Write the measure in terms of turns and describe whether they are acute, obtuse or right angles.

(a)

Angle at A = 18 turn — acute

Angle at B′ = 18 turn — acute

Angle at C (between the two lines) = 14 turn — right angle

(b)

Angle at D = 16 turn — acute

Angle at E = 14 + 112 = 412 turn — obtuse

Angle at D′ = 16 turn — acute

(c)

Angle at F = 18 turn — acute

Angle at G = 14 + 112 = 412 turn — obtuse

Angle at F′ = 14 turn — right angle

4Draw angles for the given measures of turns using the given lines.

Keep the given line as one arm. From its end point, draw the second arm after turning by the given amount.

12 turn: draw the second arm in a straight line (straight angle).

14 turn: draw the second arm at a right angle.

18 turn: draw the second arm at half of a right angle.

112 turn: draw the second arm at one-third of a right angle.

5Draw the angles formed by the following turns in your notebook.

Turn	Type of angle
12 turn	Straight angle
14 turn	Right angle
24 turn	Straight angle (same as half turn)
16 turn	Acute angle
46 turn	More than a straight angle
312 turn	Right angle (same as quarter turn)
12 + 14 turn	34 turn — more than a straight angle
18 + 16 turn	Obtuse angle

6Guess the measure of turns the minute hand of a clock makes in each case.

(a) 15 minutes → 14 turn

(b) 30 minutes → 12 turn

(d) 112 of a full turn → 5 minutes

(e) A full circle → 60 minutes

(f) 16 of a full turn → 10 minutes

(g) 412 of a full turn → 20 minutes

A full turn of the minute hand takes 60 minutes. So, each 1/12 turn takes 5 minutes.

Which Direction?

1In which direction do the hands of a clock move?

The hands of a clock move from 12 to 1, 2, 3 and so on. This is called clockwise movement.

2The creatures below have made a quarter turn once. Tick the direction in which they have moved.

Ladybird — Clockwise
Snail — Clockwise

Bee — Anti-clockwise
Ant — Anti-clockwise

3Observe the direction of movement while opening a tap, unscrewing a lid or loosening a nut. Do they move clockwise or anti-clockwise?

They all move anti-clockwise. (Closing or tightening is clockwise.)

Fun with Turns

1Complete the table by filling the direction the children will face on completing the given turns.

Starting Direction	Turns	Ending Direction
North	Two right angles, clockwise	South
South	Two right angles, anti-clockwise	North
East	Four right angles, anti-clockwise	East
West	Four right angles, clockwise	West
North	5 right angles, clockwise	East
South	3 right angles clockwise, 12 right angle clockwise, 12 right angle clockwise	South
West	2 right angles clockwise, four 12 right angles anti-clockwise	West

In the last row, the number of right angles is missing in the textbook. Four 12 right angles anti-clockwise = 2 right angles anti-clockwise. If the first turn is 2 right angles clockwise, the two turns cancel out and the child faces West again.

2Padma is facing the toy shop. What place will she face if she takes a half turn clockwise? What other way can she turn to face the same place?

After a half turn clockwise, she will face the ice cream cart.

She can also take a half turn anti-clockwise to face the same place.

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