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#### Page No 176:

#### Question 1:

Name three examples of angles from your daily life.

#### Answer:

1) Angle formed at the vertex of our elbow with the upper arm and the lower arm as the two rays. This angle will vary as per the position of our arm.

2) Angle formed between the two hands of the clock that are hinged at a point.

3) Angle formed between the two hands of a windmill. They are also hinged at a point, which is called the vertex of that angle.

#### Page No 176:

#### Question 2:

Name the vertex and the arms of ∠*ABC*, given in the figure below.

Figure

#### Answer:

The vertex is B.

Arms of $\angle ABCarerays\overrightarrow{BA}and\overrightarrow{BC}$.

#### Page No 176:

#### Question 3:

How many angles are formed in each of the figures given below? Name them.

Figure

#### Answer:

(i) Here, three angles are formed. They are $\angle ABC,\angle ACBand\angle BAC.$

(ii) Here, four angles are formed. They are $\angle ABC,\angle BCD,\angle CDAand\angle DAB$.

(iii) Here, eight angles are formed. They are $\angle ABC,\angle BCD,\angle CDA,\angle DAB,\angle ABD,\angle ADB,\angle CDB,\angle CBD$.

#### Page No 176:

#### Question 4:

In the given figure, list the points which

(i) are in the interior of ∠*AOB*

(ii) are in the interior of ∠*AOB*

(iii) lie on ∠*AOB*

Figure

#### Answer:

(i) Q and S are in the interior of $\angle $*AOB*.

(ii) P and R are in the exterior of $\angle $*AOB.*

(iii) A, O, B, N and T lie on the angle $\angle $AOB.

#### Page No 176:

#### Question 5:

See the adjacent figure and state which of the following statements are true and which are false.

(i) Point *C* is in the interior of ∠*AOC*.

(ii) Point *C* is in the interior of ∠*AOD*.

(iii) Point *D* is in the interior of ∠*AOC*.

(iv) Point *B* is in the interior of ∠*AOD*.

(v) Point *C* lies on ∠*AOB*.

Figure

#### Answer:

(i)False

Point *C* is on the angle $\angle $*AOC*.

(ii)True

Point *C lies *in the interior of $\angle $*AOD*.

(iii) False

Point *D* lies in the exterior of $\angle $*AOC*.

(iv) True

Point *B* lies in the exterior of $\angle $*AOD*.

(v) False

Point C lies in the interior of $\angle $AOB.

#### Page No 177:

#### Question 6:

In the adjoining figure, write another name for:

(i) ∠1

(ii) ∠2

(iii) ∠3

Figure

#### Answer:

(i) $\angle $EPB

(ii) $\angle $PQC

(iii) $\angle $FQD

#### Page No 179:

#### Question 1:

State the type of each of the following angles:

Figure

#### Answer:

(i) $\angle $AOB is an obtuse angle since its measure is more than 90$\xb0$.

(ii) $\angle $COD is a right angle since its measure is 90$\xb0$.

(iii) $\angle $FOE is a straight angle since its measure is 180$\xb0$.

(iv) $\angle $POQ is a reflex angle since its measure is more than 180$\xb0$ but less than 360$\xb0$.

(v) $\angle $HOG is an acute angle since its measure is more than 0 but less than 90$\xb0$.

(vi) $\angle $POP is a complete angle since its measure is 360$\xb0$.

#### Page No 179:

#### Question 2:

Classify the angles whose magnitudes are given below:

(i) 30°

(ii) 91°

(iii) 179°

(iv) 90°

(v) 181°

(vi) 360°

(vii) 128°

(viii) (90.5)°

(ix) (38.3)°

(x) 80°

(xi) 0°

(xii) 15°

#### Answer:

(i) Acute angle

This is because its measure is less than 90$\xb0$ but more than 0$\xb0$.

(ii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$

(iii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(iv)Right angle

This is because its measure is 90$\xb0$.

(v) Reflex angle

This is because its measure is more than 180$\xb0$ but less than 360$\xb0$.

(vi) Complete angle

This is because its measure is 360$\xb0$.

(vii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(viii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(ix) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

(x) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

(xi) Zero angle

This is because its measure is zero.

(xii) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

#### Page No 179:

#### Question 3:

How many degrees are there in

(i) one right angle?

(ii) two right angles?

(iii) three right angles?

(iv) four right angles?

(v) $\frac{2}{3}$ right angle?

(vi) $1\frac{1}{2}$ right angles?

#### Answer:

(i) One right angle has 90$\xb0$.

(ii) Two right angles have 90$\xb0$ + 90$\xb0$ = 180$\xb0$.

(iii) Three right angles have 90$\xb0$ + 90$\xb0$ + 90$\xb0$ = 270$\xb0$.

(iv) Four right angles have 90$\xb0$ + 90$\xb0$ + 90$\xb0$ + 90$\xb0$ = 360$\xb0$.

(v) $\frac{2}{3}\times 90=60\xb0$

(vi) $\left(1+\frac{1}{2}\right)rightangles=\frac{3}{2}\times 90\phantom{\rule{0ex}{0ex}}=135\xb0$

#### Page No 179:

#### Question 4:

How many degrees are there in the angle between the hour hand and the minute hand of a clock, when it is

(i) 3 o'clock?

(ii) 6 o'clock?

(iii) 12 o'clock?

(iv) 9 o'clock?

#### Answer:

(i) At 3 o'clock the angle formed between the hour hand and the minute hand is right angle, i.e. 90$\xb0$.

(ii) At 6 o'clock the angle formed between the hour hand and the minute hand is a straight angle, i.e. 180$\xb0$.

(iii) At 12 o'clock the angle formed between the hour hand and the minute hand is a complete angle, i.e. 0$\xb0$.

This is because the hour hand and minute hand coincides to each other at 12 o'clock.

(iv) At 9 o'clock the angle formed between the hour hand and the minute hand is a right angle, i.e. 90$\xb0$.

#### Page No 179:

#### Question 5:

Using only a ruler, draw an acute angle, an obtuse angle and a straight angle.

#### Answer:

(i) Acute angle

(ii) Obtuse angle

(iii) Straight angle

#### Page No 182:

#### Question 1:

Measure each of the following angles with the help of a protractor and write the measure in degrees:

Figure

#### Answer:

(i) $\angle AOB=45\xb0$

(ii) $\angle PQR=75\xb0$

(iii) $\angle DEF=135\xb0$

(iv) $\angle LMN=55\xb0$

(v) $\angle TSR=135\xb0$

(vi) $\angle GHI=75\xb0$

We have measured all the above angles by placing the protractor on one of the arms of the angle and measuring the angle through the other arm that coincides with the angle on the protractor.

#### Page No 182:

#### Question 2:

Construct each of the following angles with the help of a protractor:

(i) 25°

(ii) 72°

(iii) 90°

(iv) 117°

(v) 165°

(vi) 23°

(vii) 180°

(viii) 48°

#### Answer:

Steps to follow:

- Draw a ray QP with Q as the initial point.
- Place the protractor on QP. With its centre on Q, mark a point R against the given angle mark of the protractor.
- Join RQ. Now, PQR is the required angle.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

#### Page No 182:

#### Question 3:

Measure ∠*ABC* given in the adjoining figure and construct an angle *DEF* equal to ∠*ABC*.

#### Answer:

We can see that $\angle ABC=47\xb0$.

Steps to follow to construct angle $\angle $DEF equal to $\angle $ABC:

- Draw a ray EF with E as the initial point.
- Place the protractor on EF. With its centre at E, mark a point D against the angle 47$\xb0$ of the protractor.
- Join DE. $\angle $DEF = 47$\xb0$ = $\angle $ABC is the required angle.

#### Page No 182:

#### Question 4:

Draw a line segment *AB* = 6 cm. Take a point *C* on *AB* such that *AC* = 4 cm. From *C*, draw *CD* ⊥ *AB*.

#### Answer:

- Draw a line segment AB of length 6 cm.
- Mark point C on AB such that AC is equal to 4 cm.
- Place the protractor on AB such that the centre of the protractor is on C and its base lies along AB.
- Holding the protractor, mark a point D on the paper against the 90$\xb0$ mark of the protractor.
- Remove the protractor and draw a ray CD with C as the initial point.

#### Page No 182:

#### Question 1:

Where does the vertex of an angle lie?

(a) In its interior

(b) In its exterior

(c) On the angle

(d) None of these

#### Answer:

(c) On the angle

Vertex is the initial point of two rays between which the angle is formed. Therefore, it lies on the angle.

#### Page No 182:

#### Question 2:

The figure formed by two rays with the same initial point is called

(a) a ray

(b) a line

(c) an angle

(d) none of these

#### Answer:

(c) an angle

The initial point is called the vertex.

#### Page No 182:

#### Question 3:

An angle measuring 180° is called

(a) a complete angle

(b) a reflex angle

(c) a straight angle

(d) none of these

#### Answer:

(c) straight angle

#### Page No 182:

#### Question 4:

An angle measuring 90° is called

(a) a straight angle

(b) a right angle

(c) a complete angle

(d) a reflex angle

#### Answer:

(b) right angle

#### Page No 182:

#### Question 5:

An angle measuring 91° is

(a) an acute angle

(b) an obtuse angle

(c) a reflex angle

(d) none of these

#### Answer:

(b) an obtuse angle

This is because it is more than 90$\xb0$ but less than 180$\xb0$.

#### Page No 182:

#### Question 6:

An angle measuring 270° is

(a) an obtuse angle

(b) an acute angle

(c) a straight angle

(d) a reflex angle

#### Answer:

(d) a reflex angle

This is because it is more than 180$\xb0$ but less than 360$\xb0$.

#### Page No 182:

#### Question 7:

The measure of a straight angle is

(a) 90°

(b) 150°

(c) 180°

(d) 360°

#### Answer:

(c) 180$\xb0$

#### Page No 183:

#### Question 8:

An angle measuring 200° is

(a) an obtuse angle

(b) an acute angle

(c) a reflex angle

(d) none of these

#### Answer:

(c) a reflex angle

This is because it is more than 180$\xb0$ but less than 360$\xb0$.

#### Page No 183:

#### Question 9:

An angle measuring 360° is

(a) a reflex angle

(b) an obtuse angle

(c) a straight angle

(d) a complete angle

#### Answer:

(d) a complete angle

This is because it completes the rotation of 360$\xb0$.

#### Page No 183:

#### Question 10:

A reflex angle measures

(a) more than 180° but less than 270°

(b) more than 180° but less than 360°

(c) more than 90° but less than 180°

(d) none of these

#### Answer:

(b) more than 180$\xb0\mathrm{but}\mathrm{less}\mathrm{than}360\xb0$

#### Page No 183:

#### Question 11:

2 right angles = ?

(a) 90°

(b) 180°

(c) 270°

(d) 360°

#### Answer:

(b)

2 right angles = $2\times 90\xb0=180\xb0$ (straight angle)

#### Page No 183:

#### Question 12:

$\frac{3}{2}$ right angles = ?

(a) 115°

(b) 135°

(c) 270°

(d) 230°

#### Answer:

(b) 135$\xb0$

$\frac{3}{2}\mathrm{right}\mathrm{angle}=\frac{3}{2}\times 90\xb0\phantom{\rule{0ex}{0ex}}=135\xb0$

#### Page No 183:

#### Question 13:

If there are 36 spokes in a bicycle wheel, then the angle between a pair of adjacent spokes is

(a) 15°

(b) 12°

(c) 10°

(d) 18°

#### Answer:

( c) 10$\xb0$

Number of spokes = 36

Measure of the angle of the wheel = Complete angle = 360$\xb0$

Angle between a pair of adjacent spokes=$\frac{\mathrm{Measure}\mathrm{of}\mathrm{angle}}{\mathrm{Number}\mathrm{of}\mathrm{spokes}}=\frac{360\xb0}{36}=10\xb0$

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