in circle y, what is $m\angle szt$?

$86^\circ$
$94^\circ$
$108^\circ$
$128^\circ$

Question

in circle y, what is $m\angle szt$?

$86^\circ$
$94^\circ$
$108^\circ$
$128^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Angles of Intersecting Chords", "Circle Arc Measure" ], "current_concepts": [ "Angles of Intersecting Chords", "Circle Arc Measure" ] } ## Identify the intersecting chords and intercepted arcs $$ \begin{aligned} &\text{Chords } RT \text{ and } SU \text{ intersect at point } Z \text{ inside circle } Y.\ &\text{Intercepted arcs for vertical angles } \angle SZR \text{ and } \angle TZU \text{ are } \widehat{RS} = 100^\circ \text{ and } \widehat{TU} = 72^\circ. \end{aligned} $$ ## Calculate the measure of angle SZR $$ \begin{aligned} &m\angle SZR = \frac{m\widehat{RS} + m\widehat{TU}}{2}\ &m\angle SZR = \frac{100^\circ + 72^\circ}{2} = 86^\circ \end{aligned} $$ ## Calculate the measure of angle SZT $$ \begin{aligned} &m\angle SZT + m\angle SZR = 180^\circ\ &m\angle SZT = 180^\circ - 86^\circ = 94^\circ \end{aligned} $$

(A) 86°

(B) 94°

(C) 108°

(D) 128°

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

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QUESTION IMAGE

Question

Explanation:

Identify the intersecting chords and intercepted arcs

Calculate the measure of angle SZR

Calculate the measure of angle SZT

Answer: