Question

A circle is shown. Triangle J K I have points on the circle. Angle J K I is 70 degrees. The measure of arc K I is 116 degrees.
What are the measures of Arc J K and ∠KIJ?

Measure of Arc J K =
°

Measure of ∠KIJ =
°

Answer 1

Arc JI = 2·∠JKI = 2·70° = 140° (inscribed angle intercepts arc JI).
Arc JK = 360° − (arc KI + arc JI) = 360° − (116° + 140°) = 104°.
∠KIJ = 1/2 · arc KJ = 1/2 · 104° = 52°.

Measure of Arc JK = 104°
Measure of ∠KIJ = 52°