which angles are complementary to ∠adb? select all that apply.
diagram: point d with rays db, da, dc; right angle mark at ∠adb
options: ∠cda, ∠bdc, ∠cdb, ∠bda (some with checkmarks)

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# Brief Explanations:
Complementary angles sum to $90^\circ$. From the diagram, $\angle ADB + \angle BDC = 90^\circ$ (since $\angle ADC$ is right - angled? Wait, the red mark at $D$ between $AD$ and $CD$? Wait, no, looking at the diagram, $\angle ADB$ and $\angle BDC$ (or $\angle CDB$ as it's the same angle) should add up to $90^\circ$ if $\angle ADC$ is a right angle? Wait, maybe the right angle is between $AD$ and $CD$? Wait, no, the red mark is at $D$ between $BD$ and $AD$? Wait, no, let's re - examine. The angle $\angle ADB$ and $\angle BDC$ (which is the same as $\angle CDB$): if $\angle ADC$ is a right angle (the red mark), then $\angle ADB+\angle BDC = 90^\circ$, so $\angle BDC$ (or $\angle CDB$) is complementary to $\angle ADB$. Wait, maybe the initial check marks were wrong. Wait, let's think again. Complementary angles: sum to $90^\circ$. So if $\angle ADB$ and $\angle BDC$ add up to $90^\circ$ (because $\angle ADC = 90^\circ$, as per the right - angle symbol at $D$ between $AD$ and $CD$? Wait, no, the right - angle symbol is between $BD$ and $AD$? Wait, the diagram shows a right - angle mark at $D$ between $AD$ and $BD$? No, the points are $B$, $A$, $C$ with $D$ as the vertex. Let's assume that $\angle ADC$ is a right angle? No, the right - angle mark is between $AD$ and $BD$? Wait, maybe the correct angle is $\angle BDC$ (or $\angle CDB$) because $\angle ADB+\angle BDC=\angle ADC$, and if $\angle ADC = 90^\circ$, then $\angle BDC$ (same as $\angle CDB$) is complementary to $\angle ADB$. Also, maybe $\angle CDA$ is not, $\angle BDA$ is the same as $\angle ADB$, so it can't be. Wait, the original options: $\angle CDA$ is $\angle CDA$, $\angle BDC$ (same as $\angle CDB$), $\angle BDA$ is $\angle ADB$ itself. So the correct ones should be $\angle BDC$ (or $\angle CDB$) because $\angle ADB+\angle BDC = 90^\circ$ (assuming $\angle ADC = 90^\circ$). Wait, maybe the initial check marks were incorrect. Let's re - define: Complementary angles are two angles whose sum is $90^\circ$. So if $\angle ADB$ and $\angle BDC$ (which is $\angle CDB$) add up to $90^\circ$ (because $\angle ADC$ is a right angle), then $\angle BDC$ (or $\angle CDB$) is complementary to $\angle ADB$. $\angle CDA$ is not, $\angle BDA$ is the same as $\angle ADB$, so it's not. So the correct answer should be $\angle BDC$ (or $\angle CDB$). Wait, maybe the diagram has $\angle ADB$ and $\angle BDC$ forming a right angle. So the correct angles complementary to $\angle ADB$ are $\angle BDC$ (and $\angle CDB$ since they are the same angle).
# Answer:
$\angle BDC$ (or $\angle CDB$) (Note: If we consider the diagram's right - angle, $\angle ADB+\angle BDC = 90^\circ$, so $\angle BDC$ (same as $\angle CDB$) is complementary. $\angle CDA$ and $\angle BDA$ are not complementary to $\angle ADB$ ( $\angle BDA$ is $\angle ADB$ itself, and $\angle CDA$ does not sum to $90^\circ$ with $\angle ADB$ in the given diagram context). So the correct options are $\angle BDC$ and $\angle CDB$ (but they are the same angle, so the answer is $\angle BDC$ (or $\angle CDB$)). If we have to choose from the given options, the correct one is $\angle BDC$ (or $\angle CDB$).

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