In the figure below, ABCD is a square and CEFG is a rectangle. $\angle\text{GCD} = 203^\circ$. Find $\angle\text{BCE}$. Ans: ___

1. Identify the known angles around point C.

Since $ABCD$ is a square, $\angle\text{BCD} = 90^\circ$.
Since $CEFG$ is a rectangle, $\angle\text{ECG} = 90^\circ$.

2. Use the sum of angles at a point to find $\angle\text{BCE}$.

The angles around point C sum to $360^\circ$. The reflex angle $\angle\text{GCD}$ covers the outside, so the sum of the other angles equals the reflex angle.
$\text{Reflex } \angle\text{GCD} = \angle\text{BCD} + \angle\text{BCE} + \angle\text{ECG}$
$203^\circ = 90^\circ + \angle\text{BCE} + 90^\circ$
$203^\circ = 180^\circ + \angle\text{BCE}$
$\angle\text{BCE} = 203^\circ - 180^\circ = 23^\circ$