Answer: The correct option is
(A) 33°.
Step-by-step explanation: In the given figure, AB ║ CD and BC║ DE.
Also, m∠BCA = 90° and m∠BAC = 57°.
We are to find the measure of angle CDE.
We know that
the sum of the measures of the three angle of a triangle is 180°, so from triangle ABC, we have
[tex]m\angle BCA+m\angle BAC+m\angle ABC=180^\circ\\\\\Rightarrow 90^\circ+57^\circ+m\angle ABC=180^\circ\\\\\Rightarrow m\angle ABC=180^\circ-90^\circ-57^\circ\\\\\Rightarrow m\angle ABC=180^\circ-143^\circ\\\\\Rightarrow m\angle ABC=33^\circ.[/tex]
Now, since AB ║ CD and BC is a transversal so we get
[tex]m\angle ABC=m\angle BCD~[\textup{alternate interior angles}]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Similarly, since BC║ DE and CD is the tranversal, so we get
[tex]m\angle BCD=m\angle CDE~[\textup{alternate interior angles}]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equations (i) and (ii), we get
[tex]m\angle CDE=m\angle ABC=33^\circ.[/tex]
Thus, the required measure of angle CDE is 33°.
Option (A) is CORRECT.
