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Math Help - Polygon Sides

  1. #1
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    Polygon Sides

    A polygon with sides: 154-x, 50-2x, x+120, and x^2 + 7x.
    Solve for x and give each angle, if necessary.

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  2. #2
    Senior Member vincisonfire's Avatar
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    Actually it is not a polygon since it has a curve in it.
    Doing a sketch, you should easily find the angle and intersect of the lines.
    *50-2x = x +120
     -70 = 3x
     -\frac{70}{3} = x
    This is an example, it is NOT one of the vertexes.
    For the parabola, I would use the derivative to find the slope at the intersect.
    If needed ask for further explanations.
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    A polygon with sides: 154-x, 50-2x, x+120, and x^2 + 7x.
    Solve for x and give each angle, if necessary.
    Hello magentarita,

    If I were a betting person, I would bet that you meant to say angles instead of sides, because:

    154-x + 50-2x + x+120 + x^2+7x = 360

    since the sum of the angles of a quadrilateral = 360 degrees.

    Now, this all boils down to:

    x^2+5x-36=0

    (x+9)(x-4)=0

    x=-9 \ \ or \ \ x=4

    Using x=-9

    154-(-9)=163
    50-2(-9)=68
    (-9)+120=111
    (-9)^2+7(-9)=18

    Now, you try using x=4 and see what happens.
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    Thanks

    I want to thank both replies.
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    I want to thank both replies.
    Well.....was I right?!?
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  6. #6
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    yes...

    Quote Originally Posted by masters View Post
    Well.....was I right?!?
    Yes, you were right.
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  7. #7
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    Quote Originally Posted by vincisonfire View Post
    Actually it is not a polygon since it has a curve in it.
    Doing a sketch, you should easily find the angle and intersect of the lines.
    I interpreted this to mean that these were the lengths of the sides, not equations of the lines. But I suspect that masters is right and they are really supposed to be measures of the angles so that they add to 360.

    *50-2x = x +120
     -70 = 3x
     -\frac{70}{3} = x
    This is an example, it is NOT one of the vertexes.
    For the parabola, I would use the derivative to find the slope at the intersect.
    If needed ask for further explanations.
    Follow Math Help Forum on Facebook and Google+

  8. #8
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    yes......

    Yes, thank you all for your great help.
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