Correct option is B
Important Key Points:
- Adjacent Angles: Two angles are adjacent if they have a common vertex and a common arm, and do not overlap.
- Shared Arm: In this case,∠ABD\angle ABD∠ABD and ∠DBC\angle DBC∠DBC share the common armBDBD BD and have the common vertex BBB.
Knowledge Booster:
- Option A: Incorrect, ∠ABC\angle ABC∠ABC and ∠ABD\angle ABD∠ABD do not share a common arm; ∠ABC\angle ABC∠ABC is formed by the lines ABABAB and BCBCBC, whereas ∠ABD\angle ABD∠ABD is formed by the lines ABABAB and BDBDBD.
- Option C: Incorrect, ∠ABC\angle ABC∠ABC and ∠DBC\angle DBC∠DBC are not adjacent because they do not share a common arm. They are formed by the lines ABABAB, BCBCBC, and BDBDBD, but not in the way required for adjacent angles.
- Option D: Incorrect, as there are adjacent angles in the figure.





