Question

from the figure find reflex angle b o d if a b parallel CD

Answer 1

first draw a line  EF parallel to ab
AB II  CD
AB II EF 
EF II CD
AB II TO EF 
BOF=35
[ALTERNATE INTERIOR ANGLES] 
CD II EF 
DOF = 40 [ALTERNATE INTERIOR ANGLES]
HENCE BOD =35 + 40
                          =75

Answer 2

The measure of ∠BOD is 75°

GIVEN

∠ABO = 35°

∠COD = 40°

AB || CD

TO FIND

∠BOD

SOLUTION

We can simply solve the above problem as follows;

First we will draw a line EOG parallel to AB and CD.

Where,

EOG is the angle bisector of ∠BOD

Therefore,

∠BOE = 1/2 ∠BOD

∠DOE = 1/2∠BOD

Now,

AB || EOG || CD

∠ABO = ∠BOE = 35° (Alternate interior angles are equal)

And,

∠CDO = ∠DOE = 40°

∠BOD = ∠BOE + ∠DOE

= 35 + 40 = 75°

Hence, The measure of ∠BOD is 75°

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