3. PAIRS OF ANGLES
VERTICALLY OPPOSITE ANGLES
A
B
C
D
AOC and BOD,
O
form pairs of vertically opposite angles.
AOD and COB
Note : Vertically Opposite angles are EQUAL
AOC = BOD, AOD = COB
5. D
B
C
A
They have common vertex.
They have common ray.
Non-common arms should lie on
either side of common arm.
Two angles are said to be adjacent
angles if
ADB, BDC
D D
Have common vertex ‘D’.
Have common arm ray BD.
ray AD and ray DC are non
common arm lying on either
side of common arm BD
6. They have common vertex.
They have common ray.
Non-common arms should lie on
either side of common arm.
Two angles are said to be adjacent
angles if
Consider PQR and SQR
Q Q
QR is the common ray.
Non-common arms QS and QP lie on the
same side of common arm QR
R
S
Q
P
Have common vertex Q.
PQR and SQR are not adjacent angles.
8. PAIRS OF ANGLES
LINEAR PAIR ANGLES
Two adjacent angles are said to form a linear pair angle,
If their non-common rays
A
C
O
B
A
AOB and BOC are the
angles in a linear pair.
form a pair of opposite rays.
9. PAIRS OF ANGLES
LINEAR PAIR ANGLES
The sum of the measure of a linear pair angle is 180°
C
O
B
A
AOB + BOC = 180°
11. If a ray stands on a line, then the sum of the two adjacent
angles so formed is 1800 and vice–versa.
1. If, OC stands on line AB
then,
2. If
mAOC + mCOB = 1800
then,
AB is a line and OC stands on the line.
i.e. A , O , B are collinear
AOC COB
+ = 1800
AOC COB
+ = 1800
O B
A
C
12. A B
C D
AB CD
P Q
PQ CD
If
AB CD
and
PQ CD
then
AB PQ
Lines which are parallel to a given line are parallel
to each other.
14. In figure, lines AB and CD intersect at O. If
A B
O
C
D
E
AOC+BOE =70ºand BOD= 40º,find BOE
and reflex COE
Sol: AOC
But,
AOC
= 400
BOE
= 700 [ From (1) and (2) ]
= 300
COE
= 1800
+ BOE = 700
BOE – AOC
= 700
[Vertically opposite angles]
….(1)
[ BOD = 400 ]
∵
….(3)
– 400
BOE
BOE
+ BOD
+
COE
= 1800
300
+ 400
+
COE
= 1100
COE
= 1800 400
–
O 40º
AOC = BOD
Reflex of COE = 360
?
40º 30º
….(2)
– COE
300
–
Ex . : 6.1 - 1
15. In figure, lines AB and CD intersect at O. If
A B
O
C
D
E
AOC+BOE =70ºand BOD= 40º,find BOE
COE
= 1100
Reflex COE
= 250º
40º
40º
30º
Reflex COE
= 360º – 110–
and reflex COE
Sol:
Ex . : 6.1 - 1