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Math Help - Angle Problem

  1. #1
    Junior Member mathhomework's Avatar
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    Question Angle Problem

    In rectangle ABCD, AF bisects angle BAD and intersects DC at point F, angle CAF=15 degrees. Find the measure of angle DOF.
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  2. #2
    Senior Member I-Think's Avatar
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    Ans

    Angle DOF=75

    Full solution in document

    Hint: Calculate angle BAD, fill in angles as necessary then just consider triangle DOC.

    When reading the solution, insert angles as they are calculated.
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  3. #3
    Junior Member Infophile's Avatar
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    Hi !

    Since \widehat{BAF}=\widehat{FAD} and ABCD rectangle then \widehat{FAD}=45^{\circ}. And \widehat{AFD}=45^{\circ} thus AD=AF.

    But \widehat{CAF}=15^{\circ} so \widehat{BAC}=30^{\circ} and \widehat{ODF}=30^{\circ} too.

    Notice \frac{AD}{DC}=\tan(30)=\frac{1}{\sqrt{3}} that's why OD^2=\left(\frac{AD}{2}\right)^2+\left(\frac{DC}{2  }\right)^2=\frac{AD^2}{4}+\frac{3AD^2}{4}=AD^2\Rig  htarrow OD=AD.

    Finally OD=DF and \widehat{ODF}=30^{\circ} therefore \widehat{DOF}=75^{\circ}.

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  4. #4
    Junior Member mathhomework's Avatar
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    Smile

    Thank you.
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  5. #5
    Junior Member Infophile's Avatar
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    With pleasure
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