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Math Help - [SOLVED] Quadrilaterals

  1. #1
    chana
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    [SOLVED] Quadrilaterals

    in the parallelogram DEFG, the measures of angle D and angle E are in the ratio of 1:4. The measure of angle F in degrees is
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by chana
    in the parallelogram DEFG, the measures of angle D and angle E are in the ratio of 1:4. The measure of angle F in degrees is
    The angle sum of any quadrilateral is 360^\circ, so the
    angle sum of our parallelogram is 360^\circ <explain how you know this>.

    As D E F G is a parallelogram \angle D\ =\ \angle F, and \angle E\ =\ \angle G <explain how you know this>.

    Call the measure of \angle D\ \alpha, then the measure of
    \angle E is  4.\alpha <explain why this is this>.

    Then as:

    \angle D\ +\ \angle E\ +\ \angle F\ +\ \angle G\ =\ 360^\circ,

    we have:

    10.\alpha\ =\ 360^\circ

    so:

    \alpha\ =\ 36^\circ,

    which means:

    \angle F\ has degree measure 36^\circ.

    RonL
    Last edited by CaptainBlack; December 4th 2005 at 08:42 PM.
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