The diagonal of an isosceles trapezoid makes an angle of 30 with the lateral side

The diagonal of an isosceles trapezoid makes an angle of 30 with the lateral side, and with a large base an angle a (alpha). Find the angle a (alpha) if the side of the trapezoid is 4√2 and the smaller base is 4.

In the triangle ABC by the theorem of sines, we define the value of the angle ACB.

ВС / SinBAC = AB / SinACB.

SinACB = AB * SinBAC / BC = 4 * √2 * (1/2) / 4 = √2 / 2.

Then the angle ACB = arcsin (√2 / 2) = 45.

Angle CAD = AСB as criss-crossing angles at the intersection of parallel straight lines BC and AD secant AC.

Answer: Angle α is 45.