**Understanding Elementary Shapes**

**Question 1.What is the measure of**

**(i)**a right angle?

**(ii)**a straight angle?

**Solution:****(i)** 1 right angle = 90°**(ii)** 1 straight angle = 2 right angles = 2 x 90°=180°

**Question 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:****(a)** True**(b)** False**(c)** True**(d)** True**(e)** True

**Question 3.Write down the measures of**

**(a)**some acute angles.

**(b)**some obtuse angles.

(give at least two examples of each).

**Solution:****(a)** Since the measure of an acute angle < 90°. So, two acute angles may be of 60° and 30°.**(b)** Since the measure of an obtuse angle > 90°. So, two obtuse angles may be of 110° and 120°.

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

**Solution:**

On measuring the given angles using protractor, we find that

**(a)**45°

**(b)**125°

**(c)**90°

**(d)**∠1 = 40°, ∠2 = 125° and ∠3 = 95°.

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

Measure of Angle A =

Measure of Angle B =

**Solution:**

Observing the given angles, we find that

∠B > ∠A

On measuring, we find that

Measure of Angle A =40°

Measure of Angle B = 65°

∴ ∠B > ∠A.

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

**Solution:**

On observing, we find that

∠B > ∠A

On measuring, we find that

∠A = 45° and ∠B =60°

Thus, ∠B > ∠A.

**Question 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:**

**(a)**acute

**(b)**obtuse

**(c)**straight

**(d)**acute

**(e)**obtuse

**Question 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:**

On estimating without measuring, the measure of the angle shown in each figure is

**(a)**45°

**(b)**60°

**(c)**125°

**(d)**135°

On measuring with the protractor, we find their measures as under:**(a)** 40°**(b)** 65°**(c)** 130°**(d)** 135°

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

**Solution:**

The angle measure between the hands of the clock in the time shown is as under:

At 9.00 a.m. : 90°

At 1.00 p.m. : 30°

At 6.00 p.m. : 180°

**Question 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:**

Looking through a magnifying glass does not make the angle larger and so the size of the angle does not change.

**Question 11.Measure and classify each angle:**

**Solution:**

The measure of angle and its classification is recorded in the given table as under: