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Describing Angles

Describing Angles 1.16 - Solution

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On the diagram, angles GDE{\color{#0000FF}{\angle GDE}} and FDA{\color{#FF0000}{\angle FDA}} are both adjacent to FDG.{\color{#009600}{\angle FDG}}.

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