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OpenSessame

In circle O, m<R = 23. Find m<O. (The figure is not drawn to scale.)

  • 8 months ago
  • 8 months ago

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  1. Directrix
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    Angle R is an inscribed angle of a circle. Use the attached theorem to get the measure of the arc it cuts off. The intercepted arc is in blue.

    • 8 months ago
  2. Directrix
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    The measure of an inscribed angle is how related to its intercepted arc?

    • 8 months ago
  3. OpenSessame
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    I understand the theorem but how do find the length?

    • 8 months ago
  4. Directrix
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    Read the part of the attachment that says that the measure of the inscribed angle is ...... ? What comes next?

    • 8 months ago
  5. OpenSessame
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    1/2 the measue of the arc

    • 8 months ago
  6. OpenSessame
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    so multply it by two?

    • 8 months ago
  7. Directrix
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    Yes. So if angle R is 23, what is the measure of arc NQ ?

    • 8 months ago
  8. OpenSessame
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    do its 46?

    • 8 months ago
  9. Directrix
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    Yes. Next, do you see that central angle O cuts off the same arc that angle R did?

    • 8 months ago
  10. OpenSessame
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    Right so 23?

    • 8 months ago
  11. Directrix
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    No, the central angle is not 23. On the previous problem, what did we say is the measure of the central angle of a circle in relation to its intercepted arc?

    • 8 months ago
  12. OpenSessame
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    1/2

    • 8 months ago
  13. Directrix
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    No, that was the inscribed angle. We're talking central angles.

    • 8 months ago
  14. OpenSessame
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    I have no idea...

    • 8 months ago
  15. Directrix
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    Read this.

    • 8 months ago
  16. OpenSessame
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    Okay i did..

    • 8 months ago
  17. OpenSessame
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    It is the arc!

    • 8 months ago
  18. OpenSessame
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    So the Angle is 46!

    • 8 months ago
  19. Directrix
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    That is correct.

    • 8 months ago
  20. OpenSessame
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    THANK YOU SOO MUCH!

    • 8 months ago
  21. Directrix
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    You are welcome.

    • 8 months ago
  22. OpenSessame
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    https://study.ashworthcollege.edu/access/content/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_12_files/mc003-1.jpg For this wouldnt the X angle be 77?

    • 8 months ago
  23. Directrix
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    Yes.

    • 8 months ago
  24. OpenSessame
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    Because they are congruent right?

    • 8 months ago
  25. OpenSessame
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    https://study.ashworthcollege.edu/access/content/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_12_files/mc012-1.jpg This is confusing me again...

    • 8 months ago
  26. Directrix
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    There is a little bit more to it. You don't know that the angles are congruent right off the bat. Look at the two congruent chords of the circle that go with the arcs cut off by the two central angles. Because in a circle, congruent chords have congruent arcs and the two central angles cut off congruent arcs, their measures are the same.

    • 8 months ago
  27. OpenSessame
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    Okay, well thank you a lot!

    • 8 months ago
  28. Directrix
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    We have done one like that.

    • 8 months ago
  29. Directrix
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    Here's the theorem you need. ^^

    • 8 months ago
  30. Directrix
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    So, what is the equation you would write to solve the equation.

    • 8 months ago
  31. OpenSessame
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    Alright! I got it from here! Thanks man!

    • 8 months ago
  32. OpenSessame
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    X^2=5(12+5)

    • 8 months ago
  33. Directrix
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    Very good.

    • 8 months ago
  34. Directrix
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    X^2 = ?

    • 8 months ago
  35. OpenSessame
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    9.2?

    • 8 months ago
  36. OpenSessame
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    85

    • 8 months ago
  37. OpenSessame
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    Would it be 9.2 or 85???

    • 8 months ago
  38. Directrix
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    x^2 = 85 x = 9.2? Yes.

    • 8 months ago
  39. OpenSessame
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    Okay:) thanks!

    • 8 months ago
  40. Directrix
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    I'll look for you online when I'm on. I enjoyed working with you.

    • 8 months ago
  41. OpenSessame
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    Thanks same with you!

    • 8 months ago
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