Question

circle d is shown with the measures of the minor arcs. which angles are congruent? \\(\angle edh\\) and \\(\angle fdg\\) \\(\angle fde\\) and \\(\angle gdh\\) \\(\angle gdh\\) and \\(\angle edh\\) \\(\angle gdf\\) and \\(\angle hdg\\)

Explanation:

Step1: Relate central angles to arcs

The measure of a central angle equals the measure of its intercepted minor arc.

Step2: Calculate each angle's measure

• $m\angle EDH = m\overset{\frown}{EH} = 65^\circ$
• $m\angle FDG = m\overset{\frown}{FG} = 115^\circ$
• $m\angle FDE = m\overset{\frown}{FE} = 115^\circ$
• $m\angle GDH = m\overset{\frown}{GH} = 65^\circ$
• $m\angle GDF = m\overset{\frown}{FG} = 115^\circ$
• $m\angle HDG = m\overset{\frown}{GH} = 65^\circ$

Step3: Match congruent angle pairs

Compare angle measures to find equal pairs.

Answer:

$\angle FDE$ and $\angle GDH$