Answer:
[tex]\displaystyle x = 19^\circ[/tex]
Step-by-step explanation:
Since ABCD is a parallelogram, we have that DA II CB and AB II DC.
Since DA II CB, by alternate interior angles:
[tex]\displaystyle \angle ADB \cong \angle CBD[/tex]
By substitution:
[tex]\displaystyle m\angle CBD = 38^\circ[/tex]
Next, recall that the interior angles of a triangle must sum to 180°. So, for ΔCBE:
[tex]\displaystyle m\angle CBE + m\angle BEC + m\angle ECB = 180^\circ[/tex]
Solve for ∠ECB. (Note that ∠CBE and ∠CBD are the same angle.):
[tex]\displaystyle \begin{aligned} (38^\circ) + (41^\circ) + m\angle ECB & = 180^\circ \\ \\ m\angle ECB + 79 ^ \circ & = 180^\circ \\ \\ m\angle ECB & = 101^\circ\end{aligned}[/tex]
Finally, recall that opposite angles in a parallelogram are congruent. That is:
[tex]\displaystyle \angle DAB \cong \angle BCD[/tex]
∠BCD is the sum of ∠ECB and ∠ECD (x). Substitute and solve for x:
[tex]\displaystyle \begin{aligned}m\angle DAB & = m\angle ECB + x \\ \\ (120^\circ) & = (101^\circ) + x \\ \\ x & = 19^\circ \end{aligned}[/tex]
In conclusion, the measure of x is 19°.
