MHB What is the value of Angle BAD in a trapezoid with specific conditions?

[Albert1]

A trapezoid ABCD given :
(1)$\overline{AB} // \overline{CD}$
(2)$\overline{BC}\ \perp \overline{AC}$ and $\overline{BC}=\overline{AC}$
(3)$\overline{AB}=\overline{BD}$
find the value of $\angle BAD$

 

[Greg]

A trapezoid ABCD given :
(1)$\overline{AB} // \overline{CD}$
(2)$\overline{BC}\ \perp \overline{AC}$ and $\overline{BC}=\overline{AC}$
(3)$\overline{AB}=\overline{BD}$
find the value of $\angle BAD$

Spoiler

The height of trapezoid $$ABCD$$ is one-half of its base. This implies that $$\angle{ABD}=30^\circ$$. As $$\triangle{ABD}$$ is isosceles, $$\angle{BAD}=75^\circ$$.

 

[Albert1]

Spoiler

The height of trapezoid $$ABCD$$ is one-half of its base. This implies that $$\angle{ABD}=30^\circ$$. As $$\triangle{ABD}$$ is isosceles, $$\angle{BAD}=75^\circ$$.

very good solution!