Question
In a pentagon $ABCDE, AB$ is parallel to $DC$ and $\angle A: \angle E : \angle D = 3: 4: 5.$ Find angle $E$.

Answer

Let the measure of the angles are $3x, 4x$ and $5x.$
Thus
$\angle A + \angle B + \angle C + \angle D + \angle E =540^\circ$
$3 x + ( \angle B + \angle C ) + 4 x + 5 x = 540^\circ$
$12x + 180^\circ = 540^\circ$
$12x = 360^\circ$
$x = 30^\circ$
Thus the measure of angle $E$ will be $4 \times 30^\circ = 120^\circ$

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