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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.
If this helps, here is the question :)
Ok. Notice my first drawing above. The measure of an inscribed angle is half the arc.
They do tell you that BD is a diameter. Think of angle BAD. It is a straight angle. What is the measure of a straight angle?
Would I use the Inscribed Angle Theorem? I used DBC = 1/2 * 57
I think you meant 54 not 57, but that is still incorrect. What you did would be correct for angle BDC. You are being asked about angle DBC, though.
Oops, yes I meant 54.
You need to find the arc that angle DBC intercepts.
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.
A diameter is made up of two radii. |dw:1439247250424:dw|
What is the measure of the angle formed by two radii that are a diameter? Hint: think of a straight angle.
Yes. A central angle intercepts an arc of the same measure.
Arc BCD is intercepted by diameter BD. Diameter BD is a straight angle of 180 degrees, so arc BCD measures 180 degrees.
Arc BC measures 54 deg. Arc BCD measures 180 deg. What is the measure of arc CD?
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? :)
Awesome!!! Thank you so much. It makes a lot more sense now!