Question

Circle D is shown with the measures of the minor arcs.

Circle D is shown. Line segments D E, D F, D G, and D H are radii. Lines are drawn to connect the points on the circle and to create secants E F, F G, G H, and H E. The measure of arc E F is 115 degrees, the measure of arc F G is 115 degrees, the measure of arc G H is 65 degrees, and the measure of arc H E is 65 degrees.

Which angles are congruent?

∠EDH and ∠FDG
∠FDE and ∠GDH
∠GDH and ∠EDH
∠GDF and ∠HDG

Answer 1

∠GDH and ∠EDH.

Both are central angles whose intercepted arcs (GH and HE) measure 65°, so the angles are equal.