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

1. Find the interior angle $\angle GCD$.

Angles at a point sum to $360^\circ$.
$\text{Interior } \angle GCD = 360^\circ - 203^\circ = 157^\circ$

2. Use the right angles of the square and rectangle to find $\angle BCE$.

The interior angle of square $ABCD$ is $\angle BCD = 90^\circ$.
The interior angle of rectangle $CEFG$ is $\angle ECG = 90^\circ$.
From the overlapping angles, we have:
$\angle GCD = \angle BCD + \angle ECG - \angle BCE$
$157^\circ = 90^\circ + 90^\circ - \angle BCE$
$157^\circ = 180^\circ - \angle BCE$
$\angle BCE = 180^\circ - 157^\circ = 23^\circ$