Question

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

Answer 1

Let the measure of the angles are 3x, 4x and 5x.

Thus

∠A + ∠B + ∠C + ∠D + ∠E = 540°

3x + (∠B + ∠C) + 4x + 5x = 540°

12x + 180° = 540°

12x = 360°

x = 30°

Thus, the measure of angle E will be 4 × 30° = 120°