if $m\widehat{lb} = 146^{\circ}$ and $m\angle i = 49^{\circ}$, find $m\widehat{dk}$.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Secant-Secant Angle Theorem", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Secant-Secant Angle Theorem", "Circle Arc Measures", "Linear Equations" ] } ## State the theorem and given values Using the *Secant-Secant Angle Theorem* knowledge point $$ \text{m}\angle I = \frac{\text{m}\widehat{LB} - \text{m}\widehat{DK}}{2} $$ Given values: $$ \begin{aligned} \text{m}\widehat{LB} &= 146^\circ \ \text{m}\angle I &= 49^\circ \end{aligned} $$ ## Set up the equation Using the *Linear Equations* knowledge point $$ 49^\circ = \frac{146^\circ - \text{m}\widehat{DK}}{2} $$ ## Solve for the unknown arc measure Using the *Linear Equations* knowledge point $$ \begin{aligned} 98^\circ &= 146^\circ - \text{m}\widehat{DK} \ \text{m}\widehat{DK} &= 146^\circ - 98^\circ \ \text{m}\widehat{DK} &= 48^\circ \end{aligned} $$ If $\text{m}\widehat{LB} = 146^\circ$ and $\text{m}\angle I = 49^\circ$, find $\text{m}\widehat{DK}$. $\text{m}\widehat{DK} =$ $48^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Secant-Secant Angle Theorem" ] }

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Question

Explanation:

State the theorem and given values

Set up the equation

Solve for the unknown arc measure

Answer: