**Kseeb Class 6 Mathematics Chapter 5 Understanding Elementary Shapes Solutions**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students by providing Solutions for KSEEB Class 6 Mathematics chapter 5 Understanding Elementary Shapes. Here students can easily find all the solutions for Understanding Elementary Shapes Exercise 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8 and 5.9. Also here our Expert Mathematic Teacher’s solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 5 solutions. Here all the solutions are based on Karnataka State Board latest syllabus.

**Understanding Elementary Shapes Exercise 5.1 Solution : **

**(1) What is the disadvantage in comparing line segments by mere observation?**

**Solution : **

There is a chances of errors in comparing line segments by mere observation.

**(2) Why is it better to use a divider than a ruler, while measuring the length of a line segment?**

**Solution : **

Measuring the length of a line segment it is better to use divider than a ruler because correct measurement will be possible.

**(3) Draw any line segment, say AB. Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?**

**Solution : **

Yes, AB = AC + CB

Because C is ‘between’ A and B .i.e. C is the midpoint of line AB.

**Understanding Elementary Shapes Exercise 5.2 Solutions : **

**(1) What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from**

**(a) 3 to 9**

**(b) 4 to 7**

**(c) 7 to 10**

**(d) 12 to 9**

**(e) 1 to 10**

**(f) 6 to 3**

**Solution : **

(a) 3 to 9

One revolution is 360.

3 to 9 is 180 i.e. Half Revolution.

3 to 9 = 1 /2

(b) 4 to 7

One revolution is 360.

4 to 7 is 90 i.e. one fourth Revolution.

4 to 7 = 1 /4

(c) 7 to 10

One revolution is 360.

7 to 10 is 90 i.e. one fourth Revolution.

7 to 10 = 1 /4

(d) 12 to 9

One revolution is 360.

12 to 9 is 270 i.e. Three- fourth Revolution.

12 to 9 = 3 /4

(e) 1 to 10

One revolution is 360.

1 to 10 = 3 /4

(f) 6 to 3

One revolution is 360.

6 to 3 is 270 i.e. Three-fourth Revolution.

6 to 3 = 3 /4

**(2) Where will the hand of a clock stop if it**

**(a) starts at 12 and makes 1/2 of a revolution, clockwise?**

**(b) starts at 2 and makes 1/2 of a revolution, clockwise?**

**(c) starts at 5 and makes 1/4 of a revolution, clockwise?**

**(d) starts at 5 and makes 3/4 of a revolution, clockwise?**

**Solution : **

(a) Starts at 12 hand of a clock stop when 1/2 of a revolution at 6

(b) Starts at 2 hand of a clock stop when 1/2 of a revolution at 8

(c) Starts at 5 hand of a clock stop when 1/4 of a revolution at 8

(d) Starts at 5 hand of a clock stop when 3/4 of a revolution at 2

**(3) Which direction will you face if you start facing**

**(a) East and make 1/2 of a revolution clockwise?**

**(b) East and make 1 1/2 of a revolution clockwise?**

**(c) West and make 3/4 of a revolution anti-clockwise?**

**(d) South and make one full revolution?**

**Solution : **

(a) If we start facing east and make 1/2 of a revolution clockwise we are in west.

(b) If we start facing east and make 1 1/2 of a revolution clockwise we are in west.

(c) If we start facing west and make 3/4 of a revolution clockwise we are in North.

(d) If we start facing south and make one full revolution we are in South.

**(4) What part of a revolution have you turned through if you stand facing**

**(a) east and turn clockwise to face north?**

**(b) south and turn clockwise to face east?**

**(c) west and turn clockwise to face east?**

**Solution : **

(a) East and turn clockwise to face north we turned through 3/4.

(b) South and turn clockwise to face east we turned through 3/4.

(c) West and turn clockwise to face east we turned through 1/2.

**(5) Find the number of right angles turned through by the hour hand of a clock when it goes from**

**(a) 3 to 6**

**(b) 2 to 8**

**(c) 5 to 11**

**(d) 10 to 1**

**(e) 12 to 9**

**(f) 12 to 6**

**Solution : **

(a) The number of right angles turned through 3 to 6 is 1

(b) The number of right angles turned through is 2

(c) The number of right angles turned through is 2

(d) The number of right angles turned through is 1

(e) The number of right angles turned through is 3

(f) The number of right angles turned through is 2

**(6) How many right angles do you make if you start facing**

**(a) south and turn clockwise to west?**

**(b) north and turn anti-clockwise to east?**

**(c) west and turn to west?**

**(d) south and turn to north?**

**Solution : **

(a) If you start facing south and turn clockwise to west, then you make only one 1 right angle.

(b) If you start facing north and turn anticlockwise to east, then you make 3 right angles.

(c) If you start facing west and turn to west, then you make 4 right angles.

(d) If you start facing south and turn to north, then you make 2 right angles.

**(7) Where will the hour hand of a clock stop if it starts**

**(a) from 6 and turns through 1 right angle?**

**(b) from 8 and turns through 2 right angles?**

**(c) from 10 and turns through 3 right angles?**

**(d) from 7 and turns through 2 straight angles?**

**Solution : **

(a) Starts From 6 and turns through 1 right angle the hour hand of a clock stop at 9

(b) Starts From 8 and turns through 2 right angles the hour hand of a clock stop at 2

(c) Starts From 10 and turns through 3 right angles the hour hand of a clock stop at 7

(d) Starts From 7 and turns through 2 straight angles the hour hand of a clock stop at 7

**Understanding Elementary Shapes Exercise 5.4 Solutions : **

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

**Solution : **

(i) Right angle having measure is 90°.

(ii) Straight angle having measure is 180°

**(3) Write down the measures of**

**(a) some acute angles.**

**(b) some obtuse angles**

**Solution : **

(a) Acute angles are the angles less than 90°

Example : 40°, 50°, 60°

(b) Obtuse angles are the angles more than 90 degree

Example : 100°, 110°, 150°.

**(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 angle

(b) **→** Obtuse angle

(c) **→** straight angle

(d) **→** Acute angle

(e) **→** Obtuse angle.

**(11) Measure and classify each angle :**

Angle |
Measure |
Type |

∠AOB | ||

∠AOC | ||

∠BOC | ||

∠DOC | ||

∠DOA | ||

∠DOB |

**Solution : **

**● ∠AOB**

Measure – 40

Type – Acute

**● ∠AOC**

Measure – 120

Type – Obtuse

**● ∠BOC**

Measure – 90

Type – Right

**● ∠DOC**

Measure – 90

Type – Right

**● ∠DOA**

Measure – 110

Type – Obtuse

**● ∠DOB**

Measure – 180

Type – Straight

**Understanding Elementary Shapes Exercise 5.5 Solution : **

**(1) 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.**

**Solution : **

(a) The adjacent edges of a table top is model of perpendicular line.

(b) Not a model of perpendicular line.

(c) The line segments forming the letter ‘L’ is model of perpendicular line.

(d) Not a model of perpendicular line.

**(2) Let PQ be the perpendicular to the line segment XY. Let PQ and XY intersect in the point A. What is the measure of ****∠****PAY?**

**Solution : **

PQ be the perpendicular to the line segment XY.

PQ and XY intersect in the point A.

When line is perpendicular to the line segment it makes 90° angle.

Measure of ∠PAY = 90°

**(3) 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?**

**Solution : **

There are two set-squares.

One is 30° – 60° – 90° set square

Other is 45° – 45° – 90° set square.

Angle 90° is common i.e. Right angle is common between them.

**Understanding Elementary Shapes Exercise 5.6 Solution : **

**(1) 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°**

**(e) ΔXYZ with m ****∠****Y = 90° and XY = YZ.**

**(f) ΔLMN with m ****∠****L = 30°, m ****∠****M = 70° and m ****∠****N = 80°**

**Solution : **

(a) Triangle is called as Scalene Triangle.

(b) Triangle is called as Scalene Triangle

(c) Triangle is called as Equilateral Triangle.

(d) Triangle is called as Right angled Triangle

(e) Triangle is called as Isosceles Right angled Triangle.

(f) Triangle is called as Acute angled Triangle.

**(2) Match the following :**

Measures of Triangle |
Type of triangle |

(i) 3 sides of equal length |
(a) Scalene |

(ii) 2 sides of equal length |
(b) Isosceles right angled |

(iii) ll sides are of different |
(c) Obtuse angled |

(iv) 3 acute angles |
(d) Right angled |

(v) 1 right angle |
(e) Equilateral |

(vi) 1 obtuse angle |
(f) Acute angled |

(vii) 1 right angle with two sides of equal length |
(g) Isosceles |

**Solution : **

Measures of Triangle |
Type of triangle |

(i) 3 sides of equal length | (e) Equilateral |

(ii) 2 sides of equal length | (g) Isosceles |

(iii) ll sides are of different | (a) Scalene |

(iv) 3 acute angles | (f) Acute – angled |

(v) 1 right angle | (d) Right angled |

(vi) 1 obtuse angle | (c) Obtuse angled |

(vii) 1 right angle with two sides of equal length | (b) Isosceles right angled |

**Understanding Elementary Shapes Exercise 5.7**

**(1) Say True or False :**

**(a) Each angle of a rectangle is a right angle.**

**(b) The opposite sides of a rectangle are equal in length.**

**(c) The diagonals of a square are perpendicular to one another.**

**(d) All the sides of a rhombus are of equal length.**

**(e) All the sides of a parallelogram are of equal length.**

**(f) The opposite sides of a trapezium are parallel.**

**Solution : **

(a) – True

(b) – True

(c) – True

(d) – True

(e) – False

(f) – False

**(2) Give reasons for the following :**

**(a) A square can be thought of as a special rectangle.**

**(b) A rectangle can be thought of as a special parallelogram.**

**(c) A square can be thought of as a special rhombus.**

**(d) Squares, rectangles, parallelograms are all quadrilaterals.**

**(e) Square is also a parallelogram.**

**Solution : **

(a) Reason : A square has all the properties of a rectangle.

(b) Reason : A rectangle has all the properties of a parallelograms

(c) Reason : a square has all the properties of a rhombus

(d) Reason : All the few is did closed plane figures are called quadrilaterals.

(e) Reason : A square has all the properties of a parallelogram.

**(3) A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?**

**Solution : **

Regular quadrilateral : A square is a regular quadrilateral all of whose sides are equal in length and all off whose angles are equal in measure.

**Understanding Elementary Shapes Exercise 5.9 Solutions : **

**(2) What shape is**

**(a) Your instrument box?**

**(b) A brick?**

**(c) A match box?**

**(d) A road-roller?**

**(e) A sweet laddu?**

**Solution : **

(a) Shape of instrument box is cuboid.

(b) Shape of brick is cuboid.

(c) Shape of match box is cuboid.

(d) Shape of road-roller is a cylinder.

(e) Shape of laddu is Sphere.

**Next Chapter Solution : **

👉 Integers