In the given figure, AB and CD are parallel lines. O is a point such that angle CDO = 70° and angle DOB = 100°. Find angle ABO.

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Correct option is C

Given:

AB $$\parallel$$​ CD . O is a point such 

 $$\angle$$​CDO = 70° 

$$\angle$$​DOB = 100°

Solution: 

For Angle COD:

Since, AB $$\parallel$$ CD  $$\angle$$CDO = 70° ,   $$\angle$$​COD = 70° due to alternate interior angles.​​

$$\angle$$​ AOB:

$$\angle$$AOB is supplementary to $$\angle$$ DOB.
Therefore, $$\angle$$AOB = 180° - 100° = 80°.

$$\angle$$ABO: In triangle AOB, the sum of the interior angles is 180°.

So, $$\angle$$ABO = 180° - ($$\angle$$AOB + $$\angle$$ BAO).
We know $$\angle$$ AOB = 80°.

Since AB and CD are parallel,  $$\angle$$BAO = $$\angle$$ COD = 70°.
Therefore, $$\angle$$ ABO = 180° - (80° + 70°) = 30°.

Therefore, the $$\angle$$ABO is 30°.

Option (c) is right answer.