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# NCERT Solution - Lines & Angles Class 9 Notes | EduRev

## Class 9 : NCERT Solution - Lines & Angles Class 9 Notes | EduRev

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Class IX  Chapter 6 â€“ Lines and
Angles   Maths

Exercise 6.1 Question 1:
In the given figure, lines AB and CD intersect at O. If and

find
?
BOE and reflex
?
COE.

Question 2:
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1

Class IX  Chapter 6 â€“ Lines and
Angles   Maths

Exercise 6.1 Question 1:
In the given figure, lines AB and CD intersect at O. If and

find
?
BOE and reflex
?
COE.

Question 2:
Cbse-spot.blogspot.com
2

Let the common ratio between a and b be x.
a = 2x, and b = 3x
XY is a straight line, rays OM and OP stand on it.
XOM +  MOP +  POY = 180º
b + a +  POY = 180º
3x + 2x + 90º = 180º
5x = 90º x = 18º a =
2x = 2 × 18 = 36º b =
3x= 3 ×18 = 54º
MN is a straight line. Ray OX stands on it.
b + c = 180º (Linear Pair)
54º + c = 180º c = 180º -
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,
find  c .

Page 3

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1

Class IX  Chapter 6 â€“ Lines and
Angles   Maths

Exercise 6.1 Question 1:
In the given figure, lines AB and CD intersect at O. If and

find
?
BOE and reflex
?
COE.

Question 2:
Cbse-spot.blogspot.com
2

Let the common ratio between a and b be x.
a = 2x, and b = 3x
XY is a straight line, rays OM and OP stand on it.
XOM +  MOP +  POY = 180º
b + a +  POY = 180º
3x + 2x + 90º = 180º
5x = 90º x = 18º a =
2x = 2 × 18 = 36º b =
3x= 3 ×18 = 54º
MN is a straight line. Ray OX stands on it.
b + c = 180º (Linear Pair)
54º + c = 180º c = 180º -
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,
find  c .

Cbse-spot.blogspot.com
3

54º = 126º
c = 126º
Question 3:
In the given figure,  PQR =  PRQ, then prove that  PQS = PRT.

In the given figure, ST is a straight line and ray QP stands on it.
PQS +  PQR = 180º (Linear Pair)
PQR = 180º -  PQS (1)
PRT + PRQ = 180º (Linear Pair)
PRQ = 180º -  PRT (2)
It is given that  PQR =  PRQ.
Equating equations (1) and (2), we obtain

180º -

PQS = 180 - PRT PQS
= PRT
Page 4

Cbse-spot.blogspot.com
1

Class IX  Chapter 6 â€“ Lines and
Angles   Maths

Exercise 6.1 Question 1:
In the given figure, lines AB and CD intersect at O. If and

find
?
BOE and reflex
?
COE.

Question 2:
Cbse-spot.blogspot.com
2

Let the common ratio between a and b be x.
a = 2x, and b = 3x
XY is a straight line, rays OM and OP stand on it.
XOM +  MOP +  POY = 180º
b + a +  POY = 180º
3x + 2x + 90º = 180º
5x = 90º x = 18º a =
2x = 2 × 18 = 36º b =
3x= 3 ×18 = 54º
MN is a straight line. Ray OX stands on it.
b + c = 180º (Linear Pair)
54º + c = 180º c = 180º -
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,
find  c .

Cbse-spot.blogspot.com
3

54º = 126º
c = 126º
Question 3:
In the given figure,  PQR =  PRQ, then prove that  PQS = PRT.

In the given figure, ST is a straight line and ray QP stands on it.
PQS +  PQR = 180º (Linear Pair)
PQR = 180º -  PQS (1)
PRT + PRQ = 180º (Linear Pair)
PRQ = 180º -  PRT (2)
It is given that  PQR =  PRQ.
Equating equations (1) and (2), we obtain

180º -

PQS = 180 - PRT PQS
= PRT
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4

then prove that AOB is a line.
= 360º (Complete angle) It is given
that, x + y = z + w   x + y + x + y
= 360º
2(x + y) = 360º x
+ y = 180º
Since x and y form a linear pair, AOB is a line.
Question 5:
In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another
ray lying between rays OP and OR. Prove that
It can be observed that,  x + y + z + w
Question 4:
In the given figure, if

Page 5

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1

Class IX  Chapter 6 â€“ Lines and
Angles   Maths

Exercise 6.1 Question 1:
In the given figure, lines AB and CD intersect at O. If and

find
?
BOE and reflex
?
COE.

Question 2:
Cbse-spot.blogspot.com
2

Let the common ratio between a and b be x.
a = 2x, and b = 3x
XY is a straight line, rays OM and OP stand on it.
XOM +  MOP +  POY = 180º
b + a +  POY = 180º
3x + 2x + 90º = 180º
5x = 90º x = 18º a =
2x = 2 × 18 = 36º b =
3x= 3 ×18 = 54º
MN is a straight line. Ray OX stands on it.
b + c = 180º (Linear Pair)
54º + c = 180º c = 180º -
In the given figure, lines XY and MN intersect at O. If  ? POY =  and  a : b   =  2 : 3,
find  c .

Cbse-spot.blogspot.com
3

54º = 126º
c = 126º
Question 3:
In the given figure,  PQR =  PRQ, then prove that  PQS = PRT.

In the given figure, ST is a straight line and ray QP stands on it.
PQS +  PQR = 180º (Linear Pair)
PQR = 180º -  PQS (1)
PRT + PRQ = 180º (Linear Pair)
PRQ = 180º -  PRT (2)
It is given that  PQR =  PRQ.
Equating equations (1) and (2), we obtain

180º -

PQS = 180 - PRT PQS
= PRT
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4

then prove that AOB is a line.
= 360º (Complete angle) It is given
that, x + y = z + w   x + y + x + y
= 360º
2(x + y) = 360º x
+ y = 180º
Since x and y form a linear pair, AOB is a line.
Question 5:
In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another
ray lying between rays OP and OR. Prove that
It can be observed that,  x + y + z + w
Question 4:
In the given figure, if

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POR = 90º
POS + SOR = 90º
ROS = 90º - POS â€¦ (1)
QOR = 90º (As OR  PQ)
QOS - ROS = 90º
ROS = QOS - 90º â€¦ (2)
On adding equations (1) and (2), we obtain
ROS = QOS - POS 2
ROS = QOS - POS) (
Question 6:
It is given that XYZ = and XY is produced to point P. Draw a figure from the
given information. If ray YQ bisects ZYP, find XYQ and reflex QYP.

It is given that OR    PQ

?
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