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Math Help - Polygons problem

  1. #1
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    Polygons problem

    Polygons problem-0002.jpg
    What is the formula of question (a) to find y?
    and how to prove that triangle ABE is similar to triangle ADC?
    Can anyone help me, thank you.
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  2. #2
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    Re: Polygons problem

    (a) There is no "formula." It's called ​thinking.

    Consider quadrilateral BCDE. The interior angles, in counter-clockwise order, are 180-y, 40, 180 - (2y+15), and 140. These add up to 360, so set up an equation and solve for y.

    (b) Once you have found y, note that triangles ABE and ACD have an angle in common. You can probably use AAA similarity.
    Thanks from william24 and HallsofIvy
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  3. #3
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    Re: Polygons problem

    For the first problem, it should be clear that angle ACD has measure 180- 140= 40 degrees and that angle ADC has measure 180- (2y+ 15)= 165- 2y degrees. That means that Angle CAD has measure 180- 40- 165+ 2y= 2y- 25 degrees. Then, since angle AEB has measure 40 degrees, angle ABE has angle 180- 40- (2y- 25)= 165- 2y= y.
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  4. #4
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    Re: Polygons problem: I solved it!

    I couldn't resist.
    Attached Thumbnails Attached Thumbnails Polygons problem-foundit.jpg  
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  5. #5
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    Re: Polygons problem

    Lolz.
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