Our given ratio of angles is 2:4:5:7. Let common multiplying factor be x°.

Hence, ∠A = 2x°, ∠B = 4x°, ∠C = 5x° and ∠D = 7x°
Since the sum of the angles of a quadrilateral is 360°, we have:
∴ 2x + 4x + 5x + 7x = 360°

∴ 18 x = 360° ​
∴ x = 20°
∴ ∠A = 40°; ∠B = 80°; ∠C = 100°; ∠D = 140°

Hence, the measure of the angles are 40°, 80°, 100° and 140°