Answer:
<BDA = 30°
Step-by-step explanation:
Let O be the point where the diagonals AC and BD intersect.
<BOC = <AOD because the perpendicular lines make 90° angles.
Because BC and AD are parallel (property of a trapezoid) <CBO = <ODA, and <BCO = <OAD (alternate interior angles).
Because ΔBCO and ΔADO have all equal angles, they are similar triangles, meaning all the sides are in equal ratios.
Since one of the corresponding sides of the triangles are 5 and 7, the ratios of ΔBCO : ΔADO = 5 : 7.
Another one of the corresponding sides in these triangles are side CO and AO. Since CA = 6, CO : AD will equal 2.5 : 3.5 (2.5 + 3.5 = 6).
Now you know two sides in ΔADO. 7, and 3.5.
Since ΔADO is a right triangle, the "opposite to 30° angle" rule will apply. This rule states that the side opposite to a 30° angle in a right triangle will be half the hypotenuse. Since 3.5 is half of the hypotenuse, 7, you can infer that <BDA will be 30°, as it's opposite to AO, whose length is 3.5.
