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

Now, since AB ║ CD and BC is a transversal so we get
![m\angle ABC=m\angle BCD~[\textup{alternate interior angles}]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)](https://img.qammunity.org/2019/formulas/mathematics/high-school/t7hq37x4zia70bm2zos89qtus3tpu8bqvj.png)
Similarly, since BC║ DE and CD is the tranversal, so we get
![m\angle BCD=m\angle CDE~[\textup{alternate interior angles}]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)](https://img.qammunity.org/2019/formulas/mathematics/high-school/8vy9loro09mjz6zocbdmulglyqzam9x083.png)
From equations (i) and (ii), we get

Thus, the required measure of angle CDE is 33°.
Option (A) is CORRECT.