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Math Help - Help needed with Circles ( Properties-Based Questions )

  1. #1
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    Help needed with Circles ( Properties-Based Questions )

    Help needed with Circles ( Properties-Based Questions )-maths.jpg

    Greetings to Forum Members, Im kinda stucked in this question so i guess i need some help...

    The Informations :

    In the diagram, ABE, ADF, BCF and DCE are straight lines. <AED = 30degrees and <AFB = 34degrees. Find <x.

    The attempt at a solution :
    Since they are Straight Lines, < EBC = 90degrees and thus, < BCE = 60 degrees.
    Since <BCE = 60 degrees, <DCF = 60degrees ( vertically opp. angles )
    Since <DCF = 60degrees, < CDF = 180 - 34 - 60 = 86 degrees. ( sum of angles in triangle )
    Since < CDF = 86 degrees , < ADB = 180 - 86 = 94 degrees.
    Therefore, < x = 180 - 94 = 86 degrees ( angles in the opposite segment )

    The Problem :
    I counter-checked against the answer and i was wrong. Or rather, i do not have enough clues to solve this question. Can someone please ' enlighten ' me ?? Thanks


    P/S : Sorry for the inconvenience for having to view my solutions and the question separately as i have no idea on how to have the image shown together with the post.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by tgpnlyt7095 View Post
    Click image for larger version. 

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    Greetings to Forum Members, Im kinda stucked in this question so i guess i need some help...

    The Informations :

    In the diagram, ABE, ADF, BCF and DCE are straight lines. <AED = 30degrees and <AFB = 34degrees. Find <x.

    The attempt at a solution :
    Since they are Straight Lines, < EBC = 90degrees and thus, < BCE = 60 degrees.
    Since <BCE = 60 degrees, <DCF = 60degrees ( vertically opp. angles )
    Since <DCF = 60degrees, < CDF = 180 - 34 - 60 = 86 degrees. ( sum of angles in triangle )
    Since < CDF = 86 degrees , < ADB = 180 - 86 = 94 degrees.
    Therefore, < x = 180 - 94 = 86 degrees ( angles in the opposite segment )

    The Problem :
    I counter-checked against the answer and i was wrong. Or rather, i do not have enough clues to solve this question. Can someone please ' enlighten ' me ?? Thanks


    P/S : Sorry for the inconvenience for having to view my solutions and the question separately as i have no idea on how to have the image shown together with the post.
    Hi tgpnlyt7095,

    Quick question....how did you determine that angle EBC = 90 degrees? The fact that they are straight lines has no bearing on what angle is formed when they cross. Did you leave out some important GIVEN information? Is line DF tangent to the circle at C or D?

    And lines are not symbolized using 3 letters....just 2.
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