Given that the major arc $JL$ of a circle measures $300°$, which of the following best describes triangle $JLM$ inscribed in the circle with points $J$, $L$, and $M$ on the circumference?

• A. Triangle $JLM$ is an obtuse triangle because the inscribed angle opposite the major arc is less than $90°$.
• B. Triangle $JLM$ is an obtuse triangle because the inscribed angle opposite the major arc is greater than $90°$.
• C. Triangle $JLM$ is an acute triangle because all its angles are less than $90°$.
• D. Triangle $JLM$ is a right triangle because the inscribed angle opposite the major arc is exactly $90°$.

Answer: (B)

Verified step by step guidance

1. Recall that the measure of an inscribed angle in a circle is half the measure of the intercepted arc. This means if an inscribed angle intercepts an arc of measure \( \theta \), then the angle measure is \( \frac{\theta}{2} \).
2. Identify the arc opposite the inscribed angle at point \( M \). Since the major arc \( JL \) measures \( 300^\circ \), the minor arc \( JL \) (the other arc between points \( J \) and \( L \)) measures \( 360^\circ - 300^\circ = 60^\circ \).
3. Determine which arc the inscribed angle at \( M \) intercepts. The angle at \( M \) intercepts the major arc \( JL \) of \( 300^\circ \), so the measure of angle \( M \) is half of \( 300^\circ \).
4. Calculate the measure of angle \( M \) using the inscribed angle theorem: \( \text{angle } M = \frac{300^\circ}{2} \). This will give an angle greater than \( 90^\circ \), indicating an obtuse angle.
5. Since one angle of triangle \( JLM \) is obtuse (greater than \( 90^\circ \)), conclude that triangle \( JLM \) is an obtuse triangle.