【Question 10】
As shown in the figure, in square $A B C D$, extend $B A$ to $G$ such that $A G=B D$. Then the degree measure of $\angle B C G$ is $\qquad$ degrees.
【Analysis and Solution】Angle Calculation
Connect $A C$;

Since in the isosceles right triangle $A B C$, $A B=B C, \angle A B C=90^{\circ}$;

Therefore, $\angle B A C=\angle B C A=45^{\circ}$;

Since $A C=B D, A G=B D$; Therefore, $A C=A G$;
Thus, $\angle G=\angle A C G$; Since $\angle B A C=\angle G+\angle A C G$; Therefore, $\angle A C G=\angle B A C \div 2=45^{\circ} \div 2=22.5^{\circ}$;

Therefore, $\angle B C G=\angle A C G+\angle B C A=22.5^{\circ}+45^{\circ}=67.5^{\circ}$.