Question

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

Explanation:

Step1: Find the measure of central angle ∠JML

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

Step2: Analyze triangle JLM

Since \(MJ = ML\) (radii of the same circle), triangle \(JLM\) has two equal sides (\(MJ = ML\)). And \(\angle JML=60^{\circ}\). In a triangle, if two sides are equal (\(MJ = ML\)) and the included angle (\(\angle JML\)) is \(60^{\circ}\), then by the property of isosceles triangles (\(a = b\), \(\angle C=60^{\circ}\) in \(\triangle ABC\) with \(a,b\) as two - side lengths and \(\angle C\) as the included angle), all angles are equal. Using the angle - sum property of a triangle (\(\angle J+\angle L+\angle M=180^{\circ}\)) and \(\angle J=\angle L\) (because \(MJ = ML\)), we have \(2\angle J+\angle M = 180^{\circ}\). Substituting \(\angle M = 60^{\circ}\), we get \(2\angle J=120^{\circ}\), \(\angle J=\angle L = 60^{\circ}\).

Answer:

equilateral