in the diagram of circle a, what is the measure of $\angle xyz$?

$35^\circ$
$70^\circ$
$75^\circ$
$140^\circ$

Question

in the diagram of circle a, what is the measure of $\angle xyz$?

$35^\circ$
$70^\circ$
$75^\circ$
$140^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arc Measure" ], "new_concepts": [ "Secant-Tangent Angle Theorem" ], "current_concepts": [ "Arc Measure", "Secant-Tangent Angle Theorem" ] } ## Calculate the measure of the remaining arc WX $$ m\widehat{WX} = 360^\circ - 175^\circ - 105^\circ = 80^\circ $$ ## Determine the measure of the intercepted arc XZ $$ m\widehat{XZ} = 105^\circ $$ ## Apply the intersecting secant-tangent angle formula $$ m\angle XYZ = \frac{m\widehat{WXZ} - m\widehat{XZ}}{2} = \frac{(80^\circ + 175^\circ) - 105^\circ}{2} = \frac{255^\circ - 105^\circ}{2} = 75^\circ $$

(A) $35^\circ$

(B) $70^\circ$

(C) $75^\circ$

(D) $140^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the measure of the remaining arc WX

Determine the measure of the intercepted arc XZ

Apply the intersecting secant-tangent angle formula

Answer: