It may not get messy that u even can't understand, therefore I will make some heading.
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Photo one:
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Part A.
[tex] \rm \angle ABD \cong \angle DBC[/tex]
This stament is completely False.
as :-
- when ever we dive the angle of 90°, it isn't necessary they are equally divided.
- it's clearly visible that angle ABD is larger than angle DBC.
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Part B.
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[tex] \rm \angle ABD \: is \: adjacent \: to \: \angle ABC[/tex]
This stament is completely False.
as:-
- adjacent angles are those that have the same vertex and a side in common. where as here ABD is drived from angle ABC.
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Part C.
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[tex] \rm \angle ABD + \angle DBC = 90 {}^{ \circ} [/tex]
This stament is true.
as:-
- whole angle ABC is 90°. we get to know due to boxed shape angle.
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Part D.
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[tex] \rm\angle DBC = \dfrac{ABC}{2} [/tex]
This statement is completely False.
as :-
- Line BD does not go throughcorner of boxed angle.
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Photo 2:-
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So this question is little tricky.
As here angle 1 = Angle 4 = Angle 5
Therefore Angle 3 is correct Answer
