Chapter - 5- EXERCISE 5.4 - Basic Geometrical Ideas (NCERT Class 6th Maths Solution)

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

Solution/Explanation:

(i) A right angle is always of 90°

(ii) A straight angle is always of 180°

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∠ .

Solution/Explanation:

(a) True.

(b) False.

(c) True.

(d) True.

(e) True.

3. Write down the measures of 

(a) some acute angles. 

(b) some obtuse angles.

        (give at least two examples of each).

Solution/Explanation:

(a) We know that, the measure of an acute angle is always less than 90^o

.

 So, 

   45^o,50^o,55^o,60^o,65^o  all are acute angles

 (b) We know that the measure of an obtuse angle, is always, greater than  90^o  but less than 180^o

. So, 

    120^o,125^o,135^o,140^o  all are obtuse angles.

4. Measure the angles given below using the Protractor and write down the measure.

Solution/Explanation:

(a) 45o

(b) 125o

(c) 90o

(d) 60o, 90o and 125o

5. Which angle has a large measure? First estimate and then measure. 

Measure of Angle A = 

Measure of Angle B =

Solution/Explanation:

Measure of Angle A = 40^o

∘

Measure of Angle B = 65^o

∠B has larger measure.

6. From these two angles which has larger measure? Estimate and then confirm by measuring them.

Solution/Explanation:

On observing, we find that
∠B > ∠A
On measuring, we find that
∠A = 45° and ∠B =60°
Thus, ∠B > ∠A.

7. Fill in the blanks with acute, obtuse, right or straight : 

(a) An angle whose measure is less than that of a right angle is______. 

(b) An angle whose measure is greater than that of a right angle is ______. 

(c) An angle whose measure is the sum of the measures of two right angles is _____. 

(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ______. 

(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be _______.

Solution/Explanation:

(a) An angle whose measure is less than that of a right angle is acute.

(b) An angle whose measure is greater than that of a right angle is obtuse.

(c) An angle whose measure is the sum of the measures of two right angles is straight.

(d) When the sum of the measures of two angles is that of a right angle, then each one of them is acute.

(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be  obtuse. 


8. Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).


Solution/Explanation:

(a) Measure of the given along = 40o 

(b) Measure of the given along = 130o 

(c) Measure of the given along = 65o 

(d) Measure of the given along = 135o 

9. Find the angle measure between the hands of the clock in each figure : 

Solution/Explanation:

The angle measure between the hands of the clock in each figure is

(a) 90o

(b) 30o

(c) 180o

10. Investigate In the given figure, the angle measures 30°. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?

Solution/Explanation:

No, the angle doesn't change, the rays would change their length, hence the size of angle increases. 

When looked through a magnifying glass 

Angle $30°$ would remains $30°$ degrees only 

11. Measure and classify each angle :

Solution/Explanation: