• December 4th 2005, 03:19 PM
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
• December 4th 2005, 08:39 PM
CaptainBlack
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