1. **Problem statement:** Given the geometric figure with triangles and angles, we need to find: a) The triangle similar to $\triangle AGC$. b) The triangle similar to $\triangle CDE$. c) The measure of angle $\angle FCD$. 2. **Recall similarity criteria:** Triangles are similar if they have equal corresponding angles (AA criterion). 3. **a) Find $\triangle AGC \sim \triangle ?$:** - $\triangle AGC$ has angles including $\angle AGC = 27^\circ$. - Look for a triangle with the same angle measures. - Given $\angle EFC = 37^\circ$ and right angles at $F$ and $G$, and the figure's structure, $\triangle AGC$ is similar to $\triangle EFC$ by AA similarity (both have right angles and share angle measures). 4. **b) Find $\triangle CDE \sim \triangle ?$:** - $\triangle CDE$ shares angles with $\triangle FGB$ (both have right angles and corresponding angles). - By AA similarity, $\triangle CDE \sim \triangle FGB$. 5. **c) Find $m\angle FCD$:** - $\angle FCD$ is formed at point C between points F and D. - Since $\triangle AGC \sim \triangle EFC$, corresponding angles are equal. - $m\angle AGC = 27^\circ$ corresponds to $m\angle EFC = 37^\circ$. - Using triangle angle sum in $\triangle FCD$, and given right angles, calculate: $$m\angle FCD = 180^\circ - 90^\circ - 27^\circ = 63^\circ$$ **Final answers:** a) $\triangle AGC \sim \triangle EFC$ b) $\triangle CDE \sim \triangle FGB$ c) $m\angle FCD = 63^\circ$