Given \( \angle BAE : \angle BAD = 2 : 5 \). Let \( \angle BAE = 2u \) and \( \angle BAD = 5u \).<br><br>
Since ABCD is a trapezium, \( \angle BAD + \angle ADC = 180^\circ \) (interior angles between parallel lines). Also, ABE is isosceles so \( \angle BAE = \angle BEA \).<br><br>
Using the given angles in the figure and the ratio, \( 2u = 24^\circ \).<br><br>
Final Answer: 24&deg;