Question

The measure of ∠KJN is 92°. What is the measure of Arc J M K?

Answer 1

I don’t have the diagram, so I’m missing how the points/lines are placed. Can you either upload the figure or tell me which of these is true?

- Is J the center of the circle, or is J on the circle?
- Is N on the circle, inside the circle, or outside the circle? Is JN a tangent or a secant or just a chord?
- Are K, M, and J points on the circle in that order (i.e. arc J–M–K is the arc from J through M to K)?

If you can’t upload the picture, give a brief description such as “J is on the circle, N is outside and JN is a tangent” or “J is on the circle, K and N are on the circle so angle KJN is an inscribed angle,” etc.

If you want the most common interpretations:
- If angle KJN is an inscribed angle (J on the circle, K and N on the circle), then arc KN = 2·92° = 184°.
- If angle KJN is formed by a tangent at J and the chord JK, then the intercepted arc K? (the arc opposite JK) = 2·92° = 184°.

Tell me which case (or send the picture) and I’ll give the exact measure of arc J M K.