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Math Help - Finding the measure of angles in a circleeeee

  1. #1
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    Finding the measure of angles in a circleeeee

    The Problem: Given: P is the centre of the circle.
    CE is the diameter.
    ∠ 1= 35
    EAB = 100

    Partial Solution: I found the measure of every angle, with the exception of ∠5.

    Here's how I found the other angles.

    The inscribed angle is half the intercepted arc. So ∠ECB = 1/2 (EAB)

    ∠EBC = 1/2 (100) = 50
    EC, as a diameter, cuts the circle in two, making each half 180.
    So EAB + BC = 180
    ∠3 is 1/2 (BC) as the inscribed angle is half the intercepted arc.
    So ∠3 = 1/2(80) = 40
    Consider triangle EBC, with interior angles adding up to 180.
    180 -40 (∠3) -50 (∠ECB) -35 (∠1) =∠2
    ∠2 = 55


    Consider semi-circle EDC.
    EP bisects the semicircle in two 90 halves. So DC = 90

    Back to the whole circle, inscribed angle ∠4 is half intercepted arc DC, so ∠4 is 45.

    From here I'm stuck, as I can't find ∠5.
    Last edited by D. Martin; June 17th 2008 at 07:41 AM. Reason: attached diagram
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  2. #2
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    Quote Originally Posted by D. Martin View Post
    The Problem: Given: P is the centre of the circle.
    CE is the diameter.
    ∠ = 35
    EAB = 100

    Partial Solution: I found the measure of every angle, with the exception of ∠5.

    ...
    Sorry for the poor diagram.
    ...
    1. Where are the points A, B, D located?

    2. Which diagram?
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  3. #3
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    Sorry for the mess

    I'm not sure why this happened or exactly how to edit it out. I'm also trying to add that alluded diagram, which I excedes form size.
    Attached Thumbnails Attached Thumbnails Finding the measure of angles in a circleeeee-question-13.bmp  
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  4. #4
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    Quote Originally Posted by earboth View Post
    1. Where are the points A, B, D located?

    2. Which diagram?
    The points are located as indicated on the recently added diagram. The first tie I tried to attach a diagram, the diagram had too much excess blank space. Therefore, it didn't load properly.
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  5. #5
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    Your question is difficult to understand and read, mainly because of all of the improperly parsed font tags in the original post, but also because it isn't clear which angle you are referring to when you say "∠ = 35." Fix these problems, and I'm sure someone would be willing to help.

    Quote Originally Posted by D. Martin View Post
    The points are located as indicated on the recently added diagram. The first tie I tried to attach a diagram, the diagram had too much excess blank space. Therefore, it didn't load properly.
    The diagram wasn't accepted because you used an inappropriate file type. There is no reason to use an uncompressed bitmap to store this kind of image (or any image at all really, except in limited circumstances). For example, I have converted your file to the PNG format (attached), and it is now less than 0.6% of the original file size. If you aren't familiar with basic image file types, do a search for some information.

    Even though your image was accepted, it is still needlessly large and is inconvenient for people with slower connections.
    Attached Thumbnails Attached Thumbnails Finding the measure of angles in a circleeeee-fileformat.png  
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  6. #6
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    Now Diagram attached

    Here is a new diagram, as small as I could make it without lossing too much information.
    Attached Thumbnails Attached Thumbnails Finding the measure of angles in a circleeeee-question-13.png  
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