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Math Help - Help with 3 Geometry Questions

  1. #1
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    Help with 3 Geometry Questions

    Hello everyone!
    I've spent hours trying to figure out these last few Geometry questions and I can't seem to find any information on it in my text book. If anyone could offer some help I would really appreciate it. Thank you so much!

    1. In the diagram below, ABCD is a parallelogram. What is Angle BEC?
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    2. What is the value of x in the diagram below?
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    3. What are the values of n and t in the kite below?
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    a. n= 4 t= 39
    b. n= 4 t= 51
    c. n= 4.5 t= 39
    d. n=4.5 t= 51
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  2. #2
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    I only have until 9 tonight to finish these questions so I REALLY would appreciate the help. I've tried every resource I could. Please help.
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  3. #3
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    Hello, LittleLotte!

    1. In the diagram below, ABCD is a parallelogram.
    What is angle BEC?
    Code:
        A o  *  *  *  *  *  o B
           *  * 30       *  *
            *     *     *     *
             *        o E      *
              *     *     *     * 
               *  * 35       *  *
              D o  *  *  *  *  *  o C

    We are given: . \angle BAE = 30^o

    Since  AB \parallel DC. then: \angle ECD = \angle BAE .(alterate-interior angles)

    Then \angle ECD = 30^o


    In \Delta EDC, we know two angles: . \angle EDC = 35^o,\;\angle ECD = 30^o

    Hence, the third angle is: . \angle DEC \:=\:180^o - 35^o - 30^o \:=\:115^o


    \angle BEC and \angle DEC are supplementary: . \angle BEC + \angle DEC \:=\:180^o

    So we have: . \angle BEC + 115^o \:=\:180^o \quad\Rightarrow\quad\boxed{ \angle BEC \,=\,65^o}

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  4. #4
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    Quote Originally Posted by LittleLotte View Post

    2. What is the value of x in the diagram below?
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    The upper and lower triangles are identical, due to opposite corner angles being equal, touching angles equal and parallel sides equal length.

    Hence 2a+2=4 so 2a=4-2=2, a=1

    x=a+3.5=1+3.5=4.5
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  5. #5
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    Quote Originally Posted by LittleLotte View Post
    3. What are the values of n and t in the kite below?
    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting
    a. n= 4 t= 39
    b. n= 4 t= 51
    c. n= 4.5 t= 39
    d. n=4.5 t= 51

    All 3 angles in a triangle sum to 180 degrees.
    In a right-angled triangle, one angle is 90 degrees.
    180-90=90 so t and 51 degrees sum to 90 degrees, so t=90-51=39 degrees.

    If the side of length 2n equals the side below it, then the side 3n-4 equals the side n+5 in length.

    n+5=3n-4, n+5+4=3n, n+9=3n, n-n+9=3n-n=2n, 9=2n, n=9/2=4.5
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