NCERT Solutions: Understanding Elementary Shapes (Exercise 5.4, 5.5 & 5.6)

# 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 90o
(ii) a straight angle?

Ans: The measure of a straight angle is 180o

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 = 53o and m∠B = 35o then m∠A > m∠B.
Ans:
(a) True; the measure of an acute angle is less than 90o
(b) False; the measure of an obtuse angle is more than 90o but less than 180o
(c) True; the measure of a reflex angle is more than 180o
(d) True; the measure of one complete revolution is 360o
(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 = 40o and ∠B = 68o

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 45o and 55o.

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 40o, 130o, 65o and 135o

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 30o. 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:

Exercise 5.5

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

Exercise 5.6

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 = 90o
(e) ΔXYZ with m∠Y = 90o and XY = YZ
(f) ΔLMN with m∠L = 30o , m∠M = 70o and m∠N = 80o
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.

The document NCERT Solutions for Class 8 Maths Chapter 5 - Understanding Elementary Shapes (Exercise 5.4, 5.5 and 5.6) is a part of the Class 6 Course NCERT Textbooks & Solutions for Class 6.
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## FAQs on NCERT Solutions for Class 8 Maths Chapter 5 - Understanding Elementary Shapes (Exercise 5.4, 5.5 and 5.6)

 1. What are some examples of elementary shapes?
Ans. Elementary shapes are basic shapes that form the foundation of geometry. Some examples of elementary shapes are circles, triangles, squares, rectangles, and polygons.
 2. How are elementary shapes useful in everyday life?
Ans. Understanding elementary shapes is useful in everyday life as they are used in various fields such as architecture, engineering, art, and design. For example, architects use geometric shapes to design buildings and engineers use them to create bridges and other structures.
 3. How can elementary shapes be used to teach children about geometry?
Ans. Elementary shapes are a great way to introduce children to geometry as they are easy to understand and recognize. Teachers can use manipulatives such as blocks or shapes to help children learn about the different shapes, their properties, and how they can be combined to form other shapes.
 4. What is the difference between a regular and irregular polygon?
Ans. A regular polygon is a polygon that has all sides and angles equal, while an irregular polygon is a polygon that does not have all sides and angles equal. Regular polygons are often used in geometry as they have symmetrical properties, while irregular polygons are used less frequently.
 5. How can understanding elementary shapes help with problem-solving?
Ans. Understanding elementary shapes can help with problem-solving as it allows individuals to break down complex problems into simpler shapes and concepts. By identifying the shape that best represents a problem, individuals can use their knowledge of the shape's properties to find a solution.

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