Question

Circle F is congruent to circle J, and ∠EFD ≅ ∠GJH.

Circles F and J are congruent. Line segments F E and F D are radii. A line connects points E and D to form a triangle. Line segments J H and J G are radii. A line connects points H and G to form a triangle. Angles D F E and G J H are congruent.

m∠DFE = 80°. What is the measure of arc Arc G H?

Answer 1

∠DFE and ∠GJH are central angles (their vertices are the circle centers F and J). A central angle measures its intercepted arc, so m(arc DE) = 80°. Since the circles and angles are congruent, m(arc GH) = m(arc DE) = 80°.