Given the diagram, a supplement to ∠ABC could be

∠BDC
∠DAB
∠ADC
∠BAC

hn.

To find the supplement of ∠ABC, we need to find another angle that, when added to ∠ABC, will sum up to 180 degrees.

Looking at the given diagram, let's analyze the possible options:

1. ∠BDC: This could potentially be the supplement of ∠ABC. To verify, we need to check if ∠ABC + ∠BDC = 180 degrees.

2. ∠DAB: This is not the supplement of ∠ABC because it is not directly connected to ∠ABC.

3. ∠ADC: This is not the supplement of ∠ABC because it is not directly connected to ∠ABC.

4. ∠BAC: This is not the supplement of ∠ABC because it is the same angle as ∠ABC. To find the supplement, we need an angle that is different from ∠ABC.

Therefore, the correct answer is ∠BDC.

To determine the supplement of ∠ABC, we need to find another angle that, when added to ∠ABC, equals 180 degrees.

In the diagram, it's not explicitly mentioned whether it is a triangle, quadrilateral, or any other type of polygon. However, based on the options provided, it's reasonable to assume that ∠ABC is an angle within a triangle ABC.

To find the supplement of ∠ABC, we need to look for an angle that, when added to ∠ABC, equals 180 degrees.

Let's consider the given options:

1. ∠BDC: This angle is not directly related to ∠ABC, so it cannot be the supplement of ∠ABC.

2. ∠DAB: This angle is adjacent to ∠ABC, but we need to check if their sum is 180 degrees. If ∠ABC + ∠DAB = 180 degrees, then ∠DAB is the supplement of ∠ABC. If not, we need to consider the other options.

3. ∠ADC: This angle is adjacent to ∠ABC, but we need to check if their sum is 180 degrees. If ∠ABC + ∠ADC = 180 degrees, then ∠ADC is the supplement of ∠ABC. If not, we need to consider the other options.

4. ∠BAC: This angle is not adjacent to ∠ABC, so it cannot be the supplement of ∠ABC.

Based on the given options, we need to calculate ∠ABC + ∠DAB and ∠ABC + ∠ADC to check if either sum equals 180 degrees.

If ∠ABC + ∠DAB = 180 degrees, then ∠DAB is the supplement of ∠ABC.

If ∠ABC + ∠ADC = 180 degrees, then ∠ADC is the supplement of ∠ABC.

By performing these calculations, you can determine the correct supplement of ∠ABC.

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