Class 6 Maths Chapter 2 Extra Questions Lines and Angles
Class 6 Maths Lines and Angles Extra Questions
NCERT Class 6 Maths Chapter 2 Lines and Angles Extra Questions and Answers
Question 1.
Look at the figure and name the following:
(i) A line.
(ii) Four line segments with a common end-point.
(iii) Four rays having same starting points.
(iv) Five points.
Solution:
(i) \(\overleftrightarrow{\mathrm{AD}}\) is a line.
(ii)Four line segments are: \(\overline{\mathrm{OA}}\), \(\overline{\mathrm{OB}}\), \(\overline{\mathrm{OC}}\) and \(\overline{\mathrm{OD}}\). Here, the end-point O is common in all four line segments.
(iii) Four rays are: \(\overrightarrow{\mathrm{OA}}\), \(\overrightarrow{\mathrm{OB}}\), \(\overrightarrow{\mathrm{OC}}\) and \(\overrightarrow{\mathrm{OD}}\). Here O is the same starting point.
(iv) O, A, B, C, and D are five points.
Question 2.
How many lines can pass through
(i) one given point?
(ii) two given points?
(iii) three non-collinear points?
Solution:
(i) An infinite number of lines can pass through a given point O, as shown in the figure.
Note: The lines passing through a single point are called concurrent lines.
(ii) Only one line can pass through two given points as shown in the figure.
(iii) Three lines (as shown in the figure) can be drawn passing through three non-collinear points.
Note: Non-collinear points are the points that are not on the same straight line.
Question 3.
Look at the following figure and name all the rays originating from:
(i) the point A.
(ii) the point B.
(iii) the point C.
(iv) the point F .
Solution:
(i) Rays with origin A are: \(\overrightarrow{\mathrm{AF}}\), \(\overrightarrow{\mathrm{AD}}\), \(\overrightarrow{\mathrm{AB}}\), \(\overrightarrow{\mathrm{AC}}\) and \(\overrightarrow{\mathrm{AE}}\).
(ii) Rays with origin B are \(\overrightarrow{\mathrm{BC}}\), \(\overrightarrow{\mathrm{BE}}\), \(\overrightarrow{\mathrm{BA}}\), \(\overrightarrow{\mathrm{BF}}\) and \(\overrightarrow{\mathrm{BD}}\).
(iii) Rays with origin C are: \(\overrightarrow{\mathrm{CE}}\), \(\overrightarrow{\mathrm{CB}}\), \(\overrightarrow{\mathrm{CA}}\), \(\overrightarrow{\mathrm{CF}}\) and \(\overrightarrow{\mathrm{CD}}\).
(iv) Rays with origin F are: \(\overrightarrow{\mathrm{FA}}\), \(\overrightarrow{\mathrm{FB}}\), \(\overrightarrow{\mathrm{FC}}\), \(\overrightarrow{\mathrm{FD}}\) and \(\overrightarrow{\mathrm{FE}}\).
Question 4.
Name the angles in the given figure.
Solution:
The angles are:
(i) ∠A or ∠DAB
(ii) ∠B or ∠ABC
(iii) ∠C or ∠DCB
(iv) ∠D or ∠ADC
Question 5.
Draw rough diagrams of two angles such that they have
(a) One point in common.
(b) Two points in common.
(c) Three points in common.
(d) Four points in common.
(e) One ray in common.
Solution:
(a) In the figure below, ∠PQS and ∠RQT have one point Q in common.
(b) In the figure below, ∠ABC and ∠DEF have two points P and Q in common.
(c) In the figure below, ∠XQZ and ∠WPY have three points R, S and T in common.
(d) In the figure below, ∠PQR and ∠YXZ have four points A, B, C and D in common.
(e) In the figure below, ∠RQS and ∠PQS have one ray \(\overrightarrow{\mathrm{QS}}\) in common.
Question 6.
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) 3 to 6
The hour hand going from 3 to 6 turns through 1 right angle.
(b) 2 to 8
The hour hand going from 2 to 8 turns through 2 right angles.
(c) 5 to 11
The hour hand going from 5 to 11 turns through 2 right angles.
(d) 10 to 1
The hour hand going from 10 to 1 turns through 1 right angle.
(e) 12 to 9
The hour hand going from 12 to 9 turns through 3 right angles.
(f) 12 to 6
Question 7.
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) In the figure, we observe that turning clockwise from south to west, we make 1 right angle.
(b) In the figure, we find that turning anti-clockwise from north to east, we make 3 right angles.
(c) In the figure, we find that turning [clockwise or anti-clockwise] from west to west, we make 4 right angles.
(d) In the figure, we find that turning [clockwise or anti-clockwise] from south to north, we make 2 right angles.
Question 8.
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) Starting from 6 and turning through 1 right angle, the hour hand will reach at 9.
(b) Starting from 8 and turning through 2 right angles, the hour hand will reach at 2.
(c) Starting from 10 and turning through 3 right angles, the hour hand will reach at 7.
(d) Starting from 7 and turning through 2 straight angles, the hour hand will reach at 7.
Question 9.
Assertion: The sum of an acute angle and an obtuse angle may be a reflex angle.
Reason: Angles greater than 180° and less than 360°, are called reflex angles.
In the given question, a statement of Assertion is followed by a statement of Reason. Choose the correct option as:
(a) Both assertion and reason are true and the reason is the correct explanation of assertion.
(b) Both assertion and reason are true but the reason is not the correct explanation of the assertion.
(c) Assertion is true and the reason is false.
(d) Assertion is false and the reason is true.
Solution:
(b) Let the acute angle be 89° and the obtuse angle be 179°, then the sum is 89° + 179° = 268°, a reflex angle. So, the assertion is true.
Reason is also true, but the reason is not the correct explanation of the assertion.
Question 10.
Case Based Question
Mrs. Sushma, a maths teacher is guiding her class, to identify angles in English alphabets, like: three acute angles and two obtuse angles in A, two equal acute angle in letter N and so on.
Based on above information answer the following questions:
(a) Which letter represents only a right angle?
(b) Which two letters represent only four right angles?
(c) Which letter represents only two straight angles?
Solution:
(a) The letter ‘L’ represents a right angle.
(b) The letters ‘E’ and ‘H’ represents four right angles.
(c) The letter I represents two straight angles.
