Question

On circle OOO below, the measure of \stackrel{\LARGE{\frown}}{FJ} FJ ⌢ F, J, start superscript, \frown, end superscript is 84^\circ84 ∘ 84, degrees. The measure of \stackrel{\LARGE{\frown}}{GH} GH ⌢ G, H, start superscript, \frown, end superscript is 76^\circ76 ∘ 76, degrees. What is the measure of \angle HKJ∠HKJangle, H, K, J?

Answer 1

100°

Explanation:

The angle between chords is the average of the intersected arc angles.

∠FKJ = ½ (84° + 76°)

∠FKJ = 80°

∠HKJ is supplementary to ∠FKJ.

∠HKJ = 180° − 80°

∠HKJ = 100°