if $ m\widehat{sk} = 62^\circ $ and $ m\angle fgh = 64^\circ $, find $ m\widehat{fh} $.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Angles of Intersecting Chords", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Angles of Intersecting Chords", "Linear Equations" ] } ## Identify the geometric relationship $$ \text{Chords } FS \text{ and } HK \text{ intersect at point } G \text{ inside the circle.} $$ ## Apply the intersecting chords angle theorem $$ \text{m}\angle FGH = \frac{1}{2}(\text{m}\widehat{FH} + \text{m}\widehat{SK}) $$ ## Solve for the unknown arc measure $$ \begin{aligned} 64^\circ &= \frac{1}{2}(\text{m}\widehat{FH} + 62^\circ) \ 128^\circ &= \text{m}\widehat{FH} + 62^\circ \ \text{m}\widehat{FH} &= 66^\circ \end{aligned} $$ If $\text{m}\widehat{SK} = 62^\circ$ and $\text{m}\angle FGH = 64^\circ$, find $\text{m}\widehat{FH}$. $\text{m}\widehat{FH} =$ $66^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles of Intersecting Chords" ] }

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Question

Explanation:

Identify the geometric relationship

Apply the intersecting chords angle theorem

Solve for the unknown arc measure

Answer: