what is $m\angle dbt$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Angles Outside Circle Theorem", "Secant-Secant Angle" ], "new_concepts": [], "current_concepts": [ "Angles Outside Circle Theorem", "Secant-Secant Angle", "Arc Measure in Circles" ] } ## Identify the given arc measures and the angle relationship $$ \begin{aligned} &m\widehat{DT} = 138^\circ\ &m\widehat{CA} = 60^\circ \end{aligned} $$ ## Apply the Secant-Secant Angle Theorem $$ \begin{aligned} m\angle DBT &= \frac{1}{2}(m\widehat{DT} - m\widehat{CA})\ m\angle DBT &= \frac{1}{2}(138^\circ - 60^\circ) \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} m\angle DBT &= \frac{1}{2}(78^\circ)\ m\angle DBT &= 39^\circ \end{aligned} $$ What is $m\angle DBT$? 39 $^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles Outside Circle Theorem" ] }

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Question

Explanation:

Identify the given arc measures and the angle relationship

Apply the Secant-Secant Angle Theorem

Calculate the final angle measure

Answer: