Chapter 1 - Tools of Geometry - 1-5 Exploring Angle Pairs - Practice and Problem-Solving Exercises - Page 39: 34

$m\angle BCD=25$

Because $\angle FCA$ and $\angle ACD$ are a linear pair and $m\angle FCA$ is a right angle, we know that$\angle ACD$ is also a right angle. Angle Addition Postulate: $m\angle ACB+m\angle BCD=m\angle ACD$ $65+m\angle BCD=90$ $65+m\angle BCD-65=90-65$ $m\angle BCD=25$