## Understanding Elementary Shapes

## Exercise – 5.4

**Ex 5.4 Question 1.**

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

**Solution:**

(i) The measure of a right angle = 90°

(ii) The measure of a straight angle = 180°

**Ex 5.4 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 ∠B = 35°, then m∠A > m∠B.**

**Solution:**

(a) True

(b) False

(c) True

(d) True

(e) True

**Ex 5.4 Question 3.**

**Write down the measures of**

**(a) some acute angles**

**(b) some obtuse angles**

**Solution:**

(a) 25°, 50°,65°, and 72° are acute angles.

(b) 105°, 120°, 135°, and 175° are obtuse angles.

**Ex 5.4 Question 4.**

**Measure the angles given below using the protractor and write down the measure.**

**Solution:**

(a) 45°

(b) 125°

(c) 90°

(d) ∠1 = 60°, ∠2 = 90°, ∠3 = 125°

**Ex 5.4 Question 5.**

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

The measure of Angle A =

The measure of Angle B =

Solution:

The measure of Angle A = 40°

The measure of Angle B = 65°

**Ex 5.4 Question 6.**

**From these two angles which have large measures? Estimate and then confirm by measuring them.**

**Solution:**

∴ Measure of angle (a) = 45°

and the measure of angle (b) = 60°

The angle shown in the second figure is greater.

**Ex 5.4 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

**Ex 5.4 Question 8.**

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

Solution:

(a) The measure of the angle = 40°

(b) The measure of the angle = 130°

(c) The measure of the angle = 65°

(d) The measure of the angle = 135°.

**Ex 5.4 Question 9.**

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

Solution:

(i) The angle between the hour hand and the minute hand of a clock at 9.00 a.m = 90° (Right angle)

(ii) The angle between the hour hand and minute hand of a clock at 1.00 p.m = 30° (Acute angle)

(iii) The angle between the hour hand and minute hand of a clock at 6.00 p.m = 180°. (Straight angle)

**Ex 5.4 Question 10.**

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

**Solution:**

The measure of an angle will be the same.

**Ex 5.4 Question 11.**

**Measure and classify each angle:**

Angle | Measure | Type |
---|---|---|

∠AOB | ||

∠AOC | ||

∠BOC | ||

∠DOC | ||

∠DOA | ||

∠DOB |

Angle | Measure | Type |
---|---|---|

∠AOB | 40° | Acute angle |

∠AOC | 125° | Obtuse angle |

∠BOC | 85° | Acute angle |

∠DOC | 95° | Obtuse angle |

∠DOA | 140° | Obtuse angle |

∠DOB | 180° | Straight angle |