NCERT Solutions for Class 8 Maths Chapter 5 - Understanding Elementary Shapes (Exercise 5.4, 5.5 and 5.6)

Exercise 5.4

Q1. What is the measure of
(i) a right angle?
Ans: The measure of a right angle is 90^o 
(ii) a straight angle? 
Ans: The measure of a straight angle is 180^o

Q2. 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 on complete revolution = 360°. 
(e) If m∠A = 53^o and m∠B = 35^o then m∠A > m∠B. 
Ans: 
(a) True; the measure of an acute angle is less than 90^o
(b) False; the measure of an obtuse angle is more than 90^o but less than 180^o
(c) True; the measure of a reflex angle is more than 180^o
(d) True; the measure of one complete revolution is 360^o
(e) True; ∠A is greater than ∠B

Q3. Write down the measure of: 
(a) some acute angles 
(b) some obtuse angles 
(give at least two examples of each)
Ans: (a) The measures of an acute angle are 50°, 65°
(b) The measures of obtuse angle are 110°, 175°

Q4. Measure the angles given below using the Protractor and write down the measure: 

Ans: (a) The measure of an angle is 45°
(b) The measure of an angle is 120°
(c) The measure of an angle is 90°
(d) The measures of angles are 60°, 90° and 130°

Q5. Which angle has a large measure? First estimate and then measure: 

Measure of angle A = ?
Measure of angle B = ?
Ans: ∠B has larger measure.
∠A = 40^o and ∠B = 68^o

Q6. From these two angles which has larger measure? Estimate and then confirm by measuring them: 
Ans: Second angle has larger measure.
The measures of these angles are 45^o and 55^o.

Q7. Fill in the blanks with acute, obtuse, right or straight: 
(a) An angle whose measure is less than that of a right angle is ________________. 
Ans: acute angle
(b) An angle whose measure is greater than that of a right angle is ________________. 
Ans: obtuse angle
(c) An angle whose measure is the sum of the measures of two right angles is ________________. 
Ans: straight angle
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ________________. 
Ans: acute angle
(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 ________________. 
Ans: obtuse angle

Q8. Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor.) 
Ans: The measures of the angles shown in the above figures are 40^o, 130^o, 65^o and 135^o

Q9. Find the angle measure between the hands of the clock in each figure: 

Ans: (i) 90 (Right angle)
(ii) 30 (Acute angle)
(iii) 180 (Straight angle)

Q10. Investigate: 
In the given figure, the angle measure 30^o. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change? 

Ans: No, the measure of angle will be same.

Q11. Measure and classify each angle: 

Ans:

Q1. Which of the following are models for perpendicular lines:
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
(d) The letter V. 
Ans: 

(a) Perpendicular
(b) Not perpendicular
(c) Perpendicular
(d) Not perpendicular

Q2. Let   be the perpendicular to the line segment . Let  and intersect in the point A. What is the measure of ∠PAY? 
Ans: We will be using the concept of perpendicular lines to solve this.
Since PQ ⊥ XY Therefore, ∠PAY = 90°

Q3. There are two “set-squares” in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common? 

Ans: One set-square has 60°,90°, 30° and other set-square has 45° ,90° ,45°. They have 90° as common angle.

Q4. Study the diagram. The line l is perpendicular to line m. 

(a) Is CE = EG? 
(b) Does PE bisect CG? 
(c) Identify any two line segments for which PE is the perpendicular bisector. 
(d) Are these true? 
(i) AC > FG 
(ii) CD = GH 
(iii) BC < EH 
Ans: (a) Yes, both measure 2 units.
(b) Yes, because CE = EG

(d) (i) True, (ii) True, (iii) True

Q1. Name the types of following triangles: 
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm. 
(b) ΔABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm. 
(c) ΔPQR such that PQ = QR = PR = 5 cm. 
(d) ΔDEF with m∠D = 90^o 
(e) ΔXYZ with m∠Y = 90^o and XY = YZ 
(f) ΔLMN with m∠L = 30^o , m∠M = 70^o and m∠N = 80^o. 
Ans: (a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Right-angled triangle
(e) Isosceles right-angled triangle
(f) Acute-angled triangle

Q2. Match the following: 

Ans: (i) → (e)
(ii) → (g)
(iii) → (a)
(iv) → (f)
(v) → (d)
(vi) → (c)
(vii) → (b)

Q3. Name each of the following triangles in two different ways: (You may judge the nature of angle by observation) 

Ans: (i) Acute-angled and isosceles triangle
(ii) Right-angled and scalene triangle
(iii) Obtuse-angled and isosceles triangle
(iv) Right-angled and isosceles triangle
(v) Equilateral and acute-angled triangle
(vi) Obtuse-angled and scalene triangle

Q4. Try to construct triangles using match sticks. Some are shown here. 

Can you make a triangle with: 
(a) 3 matchsticks? 
(b) 4 matchsticks? 
(c) 5 matchsticks? 
(d) 6 matchsticks? 
(Remember you have to use all the available matchsticks in each case) 
If you cannot make a triangle, think of reasons for it. 
Ans: (a) 3 matchsticks This is an acute angle triangle and it is possible with 3 matchsticks to make a triangle because sum of two sides is greater than third side.
(b) 4 matchsticks This is a square, hence with four matchsticks we cannot make triangle.

(c) 5 matchsticks This is an acute angle triangle and it is possible to make triangle with five matchsticks, in this case sum of two sides is greater than third side.

(d) 6 matchsticks This is an acute angle triangle and it is possible to make a triangle with the help of 6 matchsticks because sum of two sides is greater than third side.