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|dw:1439250086914:dw|

|dw:1439246526551:dw|

54°
36°
27°
63°
I think the answer is 27, but I am unsure

Are you sure the question is angle DBC? There is no angle DBC shown in your figure.

I am sure of it. Let me take a screenshot of the question

We can find the answer. I just want to make sure we have the correct question.

|dw:1439246714171:dw|

If this helps, here is the question :)

Ok. Notice my first drawing above.
The measure of an inscribed angle is half the arc.

Would I use the Inscribed Angle Theorem?
I used DBC = 1/2 * 57

|dw:1439246922903:dw|

Oops, yes I meant 54.

You need to find the arc that angle DBC intercepts.

|dw:1439247095578:dw|

Angle DBC intercepts arc CD.
Do you see that?

I see that.

Now we need to find the measure of arc CD.
Then angle DBC is half the measure of arc CD.

|dw:1439257707805:dw|

A diameter is made up of two radii.
|dw:1439247250424:dw|

180 degrees?

Yes.
A central angle intercepts an arc of the same measure.

|dw:1439247397295:dw|

|dw:1439247431302:dw|

Arc BC measures 54 deg.
Arc BCD measures 180 deg.
What is the measure of arc CD?

126?

Great.
Now let's go back to this figure.
|dw:1439247652129:dw|

The angle you want is the inscribed angle that intercepts arc CD, so its measure is half of arc CD.

So that would be 63? :)

Exactly.

Awesome!!! Thank you so much. It makes a lot more sense now!

You're welcome.