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On the diagram, angles ${\color{#0000FF}{\angle GDE}}$ and ${\color{#FF0000}{\angle FDA}}$ are both adjacent to ${\color{#009600}{\angle FDG}}.$
The marker at $D$ indicates that ${\color{#FF0000}{\angle FDA}}$ is a right angle. This means that its linear pair, $\angle FDE,$ is also a right angle. The measure of a right angle is $90^\circ,$ so we can write an equation for the sum of the measures of ${\color{#0000FF}{\angle GDE}}$ and ${\color{#009600}{\angle FDG}}.$ $m{\color{#009600}{\angle FDG}}+m{\color{#0000FF}{\angle GDE}}=90^\circ$ Since angles are complementary if the sum of their measures is $90^\circ,$ we can conclude that ${\color{#0000FF}{\angle GDE}}$ is complementary to ${\color{#009600}{\angle FDG}}.$