## becca9898 one year ago In circle A shown below, Line BD is a diameter and the measure of Arc CB is 54°: What is the measure of ∠ DBC?

1. becca9898

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2. mathstudent55

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3. becca9898

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

4. mathstudent55

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

5. becca9898

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

6. mathstudent55

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

7. mathstudent55

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8. becca9898

9. becca9898

If this helps, here is the question :)

10. mathstudent55

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

11. mathstudent55

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?

12. becca9898

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

13. mathstudent55

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14. mathstudent55

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.

15. becca9898

Oops, yes I meant 54.

16. mathstudent55

You need to find the arc that angle DBC intercepts.

17. mathstudent55

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18. mathstudent55

Angle DBC intercepts arc CD. Do you see that?

19. becca9898

I see that.

20. mathstudent55

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

21. anonymous

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22. mathstudent55

23. mathstudent55

What is the measure of the angle formed by two radii that are a diameter? Hint: think of a straight angle.

24. becca9898

180 degrees?

25. mathstudent55

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

26. mathstudent55

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27. mathstudent55

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28. mathstudent55

Arc BCD is intercepted by diameter BD. Diameter BD is a straight angle of 180 degrees, so arc BCD measures 180 degrees.

29. mathstudent55

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

30. becca9898

126?

31. mathstudent55

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

32. mathstudent55

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

33. becca9898

So that would be 63? :)

34. mathstudent55

Exactly.

35. becca9898

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

36. mathstudent55

You're welcome.