Question

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​

Answer 1

please mark it as brainliest

Answer 2

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°*