Question

d is shown with the measures of the minor arcs. which angles are congruent? ∠edh and ∠fdg, ∠gdh and ∠edh, ∠fde and ∠gdh, ∠gdf and ∠hdg

Explanation:

Step1: Recall inscribed - angle theorem

In a circle, inscribed angles that intercept the same arc or congruent arcs are congruent.

Step2: Analyze the arcs for each pair of angles

• For ∠EDH and ∠FDG:
• ∠EDH intercepts arc EH and ∠FDG intercepts arc FG. Arc EH = 65° and arc FG = 65°. Since they intercept congruent arcs, ∠EDH and ∠FDG are congruent.
• For ∠GDH and ∠EDH:
• ∠GDH intercepts arc GH and ∠EDH intercepts arc EH. Arc GH and arc EH are not the same or congruent.
• For ∠FDE and ∠GDH:
• ∠FDE intercepts arc FE and ∠GDH intercepts arc GH. Arc FE and arc GH are not the same or congruent.
• For ∠GDF and ∠HDG:
• ∠GDF intercepts arc GF and ∠HDG intercepts arc HG. Arc GF and arc HG are not the same or congruent.

Answer:

∠EDH and ∠FDG