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Thread: Angles from Tangents

  1. #1
    Gui
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    Angles from Tangents

    Hey guys!

    I'm in need of some help again! :/ We're learning about tangents right now, I've got a test tomorrow morning. I've spent at least 5 hours in these 4 problems these past two days, and all I could figure out was 14 (55).

    Please help! Thanks in advance!

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  2. #2
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    Hi Gui, can you explain, the angles 20,35, 70 and 120 degrees.
    Between AG and AF, I can see 20 and 70 degrees. That is not clear to me.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Gui View Post
    Hey guys!

    I'm in need of some help again! :/ We're learning about tangents right now, I've got a test tomorrow morning. I've spent at least 5 hours in these 4 problems these past two days, and all I could figure out was 14 (55).

    Please help! Thanks in advance!

    Hi Gui,

    [12] Find m$\displaystyle \angle GAF$

    This angle is formed by the intersection of secants AF and AG.

    The measure of the angle is equal to the difference of the measures of the intercepted arcs.

    [13] Find $\displaystyle \angle GMH$

    This angle is formed by the tangent MH and chord MG.

    The measure of the angle is equal to one-half the measure of its intercepted arc.

    The intercepted arc here is $\displaystyle \widehat{MG}$.
    You already know the measure of $\displaystyle \widehat{FG}=70$

    You can find $\displaystyle \widehat{MF}$ easily by subtracting arcs BC, CM, and FG from 180 since BG is a diameter.

    Then add arcs FG and MF to get the intercepted arc you need. Then take half of it for your answer.

    [14] Find m$\displaystyle \angle AEM$

    This angle is formed by the intersection of two chords.
    The measure of the angle is equal to one-half the sum of the measures of the intercepted arcs.

    The intercepted arcs are CM and FG.

    Your answer is incorrect.

    [15] Find BE.

    I don't see any segment measures at all in this figure. Therefore, BE cannot be determined.
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