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Thread: [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 $\displaystyle 360^\circ$, so the
    angle sum of our parallelogram is $\displaystyle 360^\circ$ <explain how you know this>.

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

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

    Then as:

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

    we have:

    $\displaystyle 10.\alpha\ =\ 360^\circ$

    so:

    $\displaystyle \alpha\ =\ 36^\circ$,

    which means:

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

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