If the major arc $JL$ measures $300°$ in circle $M$, which of the following best describes triangle $JLM$?

• A. Right
• B. Equilateral
• C. Scalene
• D. Obtuse

Answer: (D)

Verified step by step guidance

1. Identify the given information: The major arc JL measures 300° in circle M. This means the minor arc JL measures 360° - 300° = 60°.
2. Recall that the measure of an inscribed angle is half the measure of its intercepted arc. Here, angle JML is the inscribed angle that intercepts arc JL.
3. Calculate angle JML using the formula for an inscribed angle: \(\text{angle JML} = \frac{1}{2} \times \text{measure of arc JL} = \frac{1}{2} \times 60^\circ\).
4. Determine the type of triangle JLM by considering the size of angle JML and the other angles. Since angle JML is 30°, and the triangle is formed by points on the circle, analyze the other angles accordingly.
5. Conclude that because the major arc JL is 300°, the central angle corresponding to this arc is 300°, which is obtuse (greater than 90°). Therefore, triangle JLM contains an obtuse angle, making it an obtuse triangle.