in the diagram of circle c, $m\angle vwx$ is $43^\circ$. what is $m\widehat{ux}$?

$39^\circ$
$41^\circ$
$78^\circ$
$82^\circ$

Question

in the diagram of circle c, $m\angle vwx$ is $43^\circ$. what is $m\widehat{ux}$?

$39^\circ$
$41^\circ$
$78^\circ$
$82^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Secant-Secant Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Secant-Secant Angle Theorem", "Circle Geometry", "Arc Measure" ] } ## Identify the given values and theorem $$ \begin{aligned} &m\angle VWX = 43^\circ \ &m\widehat{UY} = 128^\circ \ &m\angle VWX = \frac{1}{2}(m\widehat{UY} - m\widehat{VX}) \end{aligned} $$ ## Substitute the known values into the equation $$ 43^\circ = \frac{1}{2}(128^\circ - m\widehat{VX}) $$ ## Solve for the unknown arc measure $$ \begin{aligned} &86^\circ = 128^\circ - m\widehat{VX} \ &m\widehat{VX} = 128^\circ - 86^\circ \ &m\widehat{VX} = 42^\circ \end{aligned} $$

(A) 39°

(B) 41°

(C) 78°

(D) 82°

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given values and theorem

Substitute the known values into the equation

Solve for the unknown arc measure

Answer: