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Math·Geometry and Trigonometry·Lines, angles, and triangles

easy

Line segment $\overline{BD}$ is drawn from side $\overline{CA}$ to side $\overline{CE}$ to form triangle $CBD$. Angle $CDB$ is a right angle. Angle $CEA$ is a right angle.
In the figure shown, triangle $CAE$ is similar to triangle $CBD$. The measure of angle $CBD$ is $55^{\circ }$, and $AE=27(BD)$. What is the measure of angle $CAE$?

A

$(27\cdot 55{)}^{\circ }$

B

$(27+55{)}^{\circ }$

C

$55^{\circ }$

D

$27^{\circ }$