find the measure of the angle.

$m\angle sca =$

Question

find the measure of the angle.

$m\angle sca =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Angles Outside Circle Theorem", "Secant-Secant Angle" ], "current_concepts": [ "Angles Outside Circle Theorem", "Secant-Secant Angle" ] } ## Identify the given arc measures $$ \begin{aligned} &\text{Intercepted major arc } \widehat{SA} = 130^\circ\ &\text{Intercepted minor arc } \widehat{DB} = 48^\circ \end{aligned} $$ ## Apply the Secant-Secant Angle Theorem $$ \begin{aligned} m\angle SCA &= \frac{1}{2}(m\widehat{SA} - m\widehat{DB})\ m\angle SCA &= \frac{1}{2}(130^\circ - 48^\circ) \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} m\angle SCA &= \frac{1}{2}(82^\circ) = 41^\circ \end{aligned} $$ Find the measure of the angle. $m\angle SCA =$ $41^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles Outside Circle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given arc measures

Apply the Secant-Secant Angle Theorem

Calculate the final angle measure

Answer: