B. In the figure AB & CD are two straight lines intersecting at O, OP is a
ray. What is the measure of AOD.
a) 40°
b) 100°
c) 140°
d) 128°
Answers
Step-by-step explanation:

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________-
AB and CD intersect at O and CD is a straight line.
(i) ∠COA+ ∠AOD = 180° (linear pair)
42°+ ∠AOD = 180°
∠AOD = 138°_____answer
(ii) ∠COA and ∠BOD are vertically opposite angles.
∴∠COA = ∠BOD = 42° [from (i)]
(iii) ∠COB and ∠AOD are vertically opposite angles.
∴∠COB = ∠AOD = 138° [from (i)]
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Given:-
AB and CD are two straight lines intersecting at O.
OP is a ray.
To Find:- Angle AOD
Solution-
- AB and CD intersect at O and CD is a straight line.
- (i) ∠COA+ ∠AOD = 180° (linear pair)
42°+ ∠AOD = 180°
∠AOD = 138°
- (ii) ∠COB and ∠AOD are vertically
opposite angles.
∴∠COB = ∠AOD = 138° [from (i)]
- (iii) ∠COA and ∠BOD are vertically
opposite angles
∴ ∠COA = ∠BOD = 42° [from (i)]
- Sum of angles formed at the point is 360°.
∠COB + ∠AOD + ∠COA + ∠BOD = 360°
138° + 138° + 42° + 42° = 360°
360° = 360°
-*So, ∠AOD = 138°*