NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
Here,
It is given that,
Hence, from Eq. (i),
Now, by Linear pair axiom,
By substituting the values, we get
Now, so as to find the reflex angle,
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
It is given that,
Now, by Linear pair axiom,
So, we get, a + b =
It is also given that,
a :b = 2:3
Let a = 2k and b = 3k,
From eq. (i),
2k + 3k =
So, a = 2 ×
and b = 3 ×
Again by Linear pair axiom,
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
By Linear pair axiom,
Similarly, again by Linear pair axiom,
Thus by Eq. (i) and (ii),we get,
As it is given,
By cancelling equal terms,
we get,
Hence, proved.
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
Since, x,y,w and z are angles at a single point,
x + y + w + z =
But it is given that, x + y = w + z
Hence, by converse of linear pair axiom, it is proved that AOB is a straight line.
Q5 )
5.In figure below, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR.
Prove that
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
Since it is given that, OR is perpendicular to PQ, we have,
Also, we can say that,
Now, by adding,
2
Hence, proved.
Q6 )
It is given that
If ray YQ bisects
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
Given that, ray YQ bisects
Thus,
By Linear pair axiom,
But, it is given that,
Therefore, from (i) and (ii), we get,
Now,
Now,
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
Here, these are corresponding angles for lines AB and CD.
Hence, it is proved that AB || CD.
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
It is given that, y : z = 3:7
Let, y = 3k and z = 7k,
x =
Z =
From (i) and (ii), we get,
Now, x + y =
From eq.(iii),
z + y =
Hence, x =
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
But it is given that,
Also,
Also, by linear pair axiom, we get,
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
Construction : Draw a line parallel to ST through R.
As it is given that,
PQ || ST,
We can also say that, AB || PQ || ST
....(interior angles on the same side of
transversal)
As,
Now, so as to find
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
We have, AB || CD
Now, as we know that, Exterior angle is equal to sum of interior opposite angles of a triangle.
from (i), we get,
Q6 )
In figure, PQ and RS are two mirrors placed parallel to each other. An incident ray
AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror
RS at C and again reflects back along CD. Prove that AB || CD.
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
Draw perpendiculars BE and CF on PQ and RS, respectively.
Therefore, we can say that BE || CF
As angle of incidence = angle of reflection,
we get,
Similarly, we get,
By Alternate angles theorem,
Now, doubling the angles, we get,
2
from (i) and (ii),
Hence,
Thus by converse of alternate angles theorem,
we get, AB || CD
Hence, it is proved.
Q1 )
In figure, sides QP and RQ of
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles
Answer :
By linear pair axiom,
We also know that, Sum of interior opposite angles is equal to exterior angles.