circle d is shown with the measures of the minor arcs. which angles are congruent? ∠edh and ∠fdg ∠fde and…

Explanation:

Step1: Recall angle - arc relationship

In a circle, central angles are congruent if and only if their intercepted arcs are congruent.

Step2: Analyze the intercepted arcs

The measure of arc $EH = 65^{\circ}$, arc $HG=65^{\circ}$, arc $GF = 115^{\circ}$, arc $FE = 115^{\circ}$. $\angle FDE$ intercepts arc $FE$ and $\angle GDH$ intercepts arc $HG$. $\angle FDE$ and $\angle GDH$ are central - angles. Since arc $FE$ and arc $HG$ are not congruent, $\angle FDE$ and $\angle GDH$ are not congruent. $\angle GDH$ intercepts arc $HG$ and $\angle EDH$ intercepts arc $EH$. Since arc $HG$ and arc $EH$ are not congruent, $\angle GDH$ and $\angle EDH$ are not congruent. $\angle GDF$ intercepts arc $GF$ and $\angle HDG$ intercepts arc $HG$. Since arc $GF$ and arc $HG$ are not congruent, $\angle GDF$ and $\angle HDG$ are not congruent. $\angle EDH$ intercepts arc $EH$ and $\angle FDG$ intercepts arc $FG$. The measure of arc $EH=65^{\circ}$ and the measure of arc $FG = 65^{\circ}$. Since the intercepted arcs of $\angle EDH$ and $\angle FDG$ are congruent, $\angle EDH\cong\angle FDG$.

Answer:

$\angle EDH$ and $\angle FDG$