We have to relate the angles of the trapezoid in order to find the measure of BAD.
Given:
[tex]\begin{gathered} AB\mleft\Vert DC\mright? \\ AD\cong BC \end{gathered}[/tex]
Then
[tex]\begin{gathered} \angle BAD\cong\angle ABC \\ \angle ADC\cong\angle BCD \end{gathered}[/tex]
The angles are congruent because if AD and BC are congruent, and the lines are parallel, they sides will form the same angles.
Also, as the segment AD is "cut" by two parallel lines, the angles BAD and ADC are consecutive interior angles and are, therefore, supplementary.
Then, we can write:
[tex]\begin{gathered} m\angle BAD+m\angle ADC=180\degree\text{ and }\angle ADC=\angle BCD \\ \Rightarrow m\angle BAD+m\angle BCD=180\degree \\ 2x+(3x-5)=180 \\ 5x-5=180 \\ 5x=180+5 \\ 5x=185 \\ x=\frac{185}{5} \\ x=37 \end{gathered}[/tex]
Now, with the value of x, we can calculate the measure of BAD as:
[tex]m\angle BAD=2x=2\cdot37=74\degree[/tex]
Answer: the measure of BAD is 74°.
