in circle y, what is $m\widehat{tu}$?

$59^\circ$
$67^\circ$
$71^\circ$
$118^\circ$

Question

in circle y, what is $m\widehat{tu}$?

$59^\circ$
$67^\circ$
$71^\circ$
$118^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Angles of Intersecting Chords", "Circle Arc Measure" ], "new_concepts": [], "current_concepts": [ "Angles of Intersecting Chords", "Circle Arc Measure" ] } ## Apply the intersecting chords theorem $$ \theta = \frac{m\widehat{RS} + m\widehat{TU}}{2} $$ ## Substitute the given values $$ 63^\circ = \frac{55^\circ + m\widehat{TU}}{2} $$ ## Solve for the unknown arc measure $$ \begin{aligned} 126^\circ &= 55^\circ + m\widehat{TU} \ m\widehat{TU} &= 71^\circ \end{aligned} $$

(A) 59°

(B) 67°

(C) 71°

(D) 118°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Angles of Intersecting Chords" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the intersecting chords theorem

Substitute the given values

Solve for the unknown arc measure

Answer: