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3. Write down the measures of

(a) some acute angles.

(b) some obtuse angles.

(give at least two examples of each).

(a) 30o, 45o and 60o (b) 120o, 135o and 150o

2.  Say True or False :

(a) The measure of an acute angle < 90°.

(b) The measure of an obtuse angle < 90°.

(c) The measure of a reflex angle > 180°.

(d) The measure of one complete revolution = 360°.

(e) If m A∠ = 53° and m B∠ = 35°, then m A∠ > m B.

(a) True. (b) False. (c) True. (d) True. (e) True.

1. What is the measure of (i) a right angle? (ii) a straight angle?

(i) 90o (ii) 180o

2.  Classify each one of the following angles as right, straight, acute, obtuse or reflex :

(a) Acute. (b) Obtuse. (c) Right. (d) Reflex. (e) Straight. (f) Acute, acute.

1. Match the following :

 (i) Straight angle (a) Less than one-fourth of a revolution (ii) Right angle (b) More than half a revolution (iii) Acute angle (c) Half of a revolution (iv) Obtuse angle (d) One-fourth of a revolution (v) Reflex angle (e) Between  $\frac{1}{4}$  and  $\frac{1}{2}$  of a revolution (f) One complete revolution

(i) Straight angle  (c) Half of a revolution (ii) Right angle      (d) One-fourth of a revolution (iii) Acute angle (a) Less than one-fourth of a revolution (iv) Obtuse angle    (e) Between    and    of a revolution (v) Reflex angle    (b) More than half a revolution

7.  Where will the hour hand of a clock stop if it starts

(a) from 6 and turns through 1 right angle?

(b) from 8 and turns through 2 right angles?

(c) from 10 and turns through 3 right angles?

(d) from 7 and turns through 2 straight angles?

(a) Starting from 6 and turns through 1 right angle the hour hand stops at 9. (b) Starting from 8 and turns through 2 right angle sthe hour hand stops at 2. (c) Starting from 10 and turns through 3 right angle the hour hand stops at 7. (d) Starting from 7 and turns through 2 straight angle the hour hand stops at 7.

6.  How many right angles do you make if you start facing

(a) south and turn clockwise to west?

(b) north and turn anti-clockwise to east?

(c) west and turn to west?

(d) south and turn to north?

The number of right angles we can make from the given conditions are- (a) 1. (b) 3. (c) 4. (d) 2.

5.  Find the number of right angles turned through by the hour hand of a clock when it goes from

(a) 3 to 6                                 (b) 2 to 8                          (c) 5 to 11

(d) 10 to 1                               (e) 12 to 9                        (f) 12 to 6

Number of right angles turned through by the hour hand of a clock when it goes from (a) 3 to 6,   (b) 2 to 8,   (c) 5 to 11,  (d) 10 to 1,   (e) 12 to 9,  (f) 12 to 6  are (a) 1. (b) 2. (c) 2. (d) 1. (e) 3. (f) 2.

4. What part of a revolution have you turned through if you stand facing

(a) east and turn clockwise to face north?

(b) south and turn clockwise to face east?

(c) west and turn clockwise to face east?

(a) If we are standing facing east and turn clockwise to face north we have turned through  of a revolution. (b)  If we are standing facing south and turn clockwise to face east we have turned through   of a revolution. (c) If we are standing facing west and turn clockwise to face east we have turned through half of a revolution.

3.  Which direction will you face if you start facing

(a) east and make  $\frac{1}{2}$  of a revolution clockwise?

(b) east and make  $1\frac{1}{2}$   of a revolution clockwise?

(c) west and make  $\frac{3}{4}$  of a revolution anti-clockwise?

(d) south and make one full revolution?

(Should we specify clockwise or anti-clockwise for this last question? Why not?)

(a) West. (b) West. (c) North. (d) South. No need to specify clockwise or anti-clockwise for the last question as after one complete revolution we would be facing in the same direction.

2. Where will the hand of a clock stop if it

(a) starts at 12 and makes  $\frac{1}{2}$   of a revolution, clockwise?

(b) starts at 2 and makes  $\frac{1}{2}$   of a revolution, clockwise?

(c) starts at 5 and makes  $\frac{1}{4}$  of a revolution, clockwise?

(d) starts at 5 and makes  $\frac{3}{4}$   of a revolution, clockwise?

(a) The hand of a clock will stop at 6 after starting at 12 and making    of a revolution, clockwise. (b) The hand of a clock will stop at 8 after starting at 2 and making    of a revolution, clockwise. (c) The hand of a clock will stop at 8 after starting at 5 and making    of a revolution, clockwise. (d) The hand of a clock will stop at 2 after starting at 5 and making    of a revolution, clockwise.

1. What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from

(a) 3 to 9                       (b) 4 to 7                  (c) 7 to 10

(d) 12 to 9                     (e) 1 to 10                (f) 6 to 3

(a) Half. (b) One fourth. (c) One fourth. (d) Three fourth. (e) Three fourth. (f) Three fourth.

7. Draw five triangles and measure their sides. Check in each case, if the sum of the lengths of any two sides is always less than the third side.

After measuring their sides we have found that the sum of lengths of any two sides of a triangle is always greater than the third side.

6.  If B is the mid point of AC and C is the mid point of BD, where A,B,C,D lie on a straight line, say why AB = CD?

To Prove B is the mid point of AC              C is the mid point of BD              From (i) and (ii) we can conclude  Hence proved.

5. Verify, whether D is the mid point of AG .

AD = 4 - 1 = 3 DG = 7 - 4 = 3 Therefore AD = DG Therefore D is the midpoint of AG.

4. If A,B,C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one of them lies between the other two?

AB = 5 cm BC = 3 cm AC = 8 cm Therefore AB + BC = AC Therefore point B lies between points A and C.

3.  Draw any line segment, say AB. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?

[Note : If A,B,C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B.]

Yes

2.  Why is it better to use a divider than a ruler, while measuring the length of a line segment?

While measuring the length of a line segment using error might creep in due to the thickness and translucency of the ruler and because of angular viewing. We can get rid of these errors using a divider.

1.  What is the disadvantage in comparing line segments by mere observation?

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