in the diagram of circle a, what is $m\angle lmn$?

$75^\circ$
$90^\circ$
$120^\circ$
$135^\circ$

Question

in the diagram of circle a, what is $m\angle lmn$?

$75^\circ$
$90^\circ$
$120^\circ$
$135^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circumscribed Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Circumscribed Angle Theorem", "Arc Measure" ] } ## Calculate the measure of the intercepted minor arc $$ \begin{aligned} \text{Major Arc Measure} &= 270^\circ \ \text{Minor Arc Measure} &= 360^\circ - 270^\circ = 90^\circ \end{aligned} $$ ## Apply the Circumscribed Angle Theorem $$ \begin{aligned} m\angle LMN + \text{Minor Arc Measure} &= 180^\circ \ m\angle LMN + 90^\circ &= 180^\circ \ m\angle LMN &= 90^\circ \end{aligned} $$

(A) $75^\circ$

(B) $90^\circ$

(C) $120^\circ$

(D) $135^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circumscribed Angle Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the measure of the intercepted minor arc

Apply the Circumscribed Angle Theorem

Answer: