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

2. 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