Question

major arc jl measures 300°. which describes triangle jlm? right equilateral scalene obtuse

Explanation:

Step1: Find the measure of central angle

The sum of major arc and minor arc is \(360^{\circ}\). Given major arc \(JL = 300^{\circ}\), then minor arc \(JL=360^{\circ}-300^{\circ}=60^{\circ}\). So, \(\angle JML = 60^{\circ}\) (central angle equals the measure of its corresponding arc).

Step2: Analyze the sides of \(\triangle JLM\)

Since \(JM\) and \(LM\) are radii of the circle, \(JM = LM\). And \(\angle JML=60^{\circ}\).
In a triangle, if two sides are equal (\(JM = LM\)) and the included angle (\(\angle JML\)) is \(60^{\circ}\), then by the property of isosceles triangles (\(a = b\), \(\angle C=60^{\circ}\)), using the law of cosines \(JL^{2}=JM^{2}+LM^{2}-2\cdot JM\cdot LM\cdot\cos\angle JML\). Let \(JM = LM = r\), then \(JL^{2}=r^{2}+r^{2}-2r\cdot r\cdot\cos60^{\circ}=r^{2}+r^{2}-2r^{2}\times\frac{1}{2}=r^{2}\), so \(JL = r\).

Answer:

equilateral