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 Solution: |
| 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 |
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