Explanation

In this figure, if \(<BDC = 90\) degrees than \(<BDO\) should be \(90\) degrees as well.
This is because angle in a straight line add to \(180\) degree

Similarly, If \(<AOB = 44\)degrees than \(<BOD = 46\) degrees because Given \(AOC\) is a right triangle so \(<AOB\) and \(<BOD\) should add to \(90\)degrees

Now the remaining angle\(<DBO = 44\) degrees
Sum of angles in a triangle add to \(180\) degrees.

From here we can deduce that \(BD>OD\) because side opposite larger angle is larger than side opposite smaller angle in a triangle
option B
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Given: ∠AOC = 90°
So, if ∠AOB = 44°, then ∠BOD = 46°

If ∠BOD = 46°, then ∠OBD = 44° (since all 3 angles in ∆OBD must add to 180°

Notice that side OD is opposite the 44° angle (aka ∠OBD),
and side BD is opposite the 46° angle (aka ∠BOD)

Since 46° > 44°, we can conclude that side BD > side OD

Answer: B

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Opposite of larger angle is larger side

B

Nice it is B.
We can determine which side is greater by its correspondent angle.
BD is bigger since its correspondent angle is 46
and OD is smaller since its correspondent angle is 44

Compare angles and opposite sides: angle 46 is opposite to BD, and angle 44 (from right triangle BOD, adjacent angle BDO=90 (=180-90) is opposite to OD. BD>OD and Quantity B is greater. Answer is B.