solve for x
$ (4x + 2)^\circ $
$ (9x - 3)^\circ $
$ x = \underline{\quad\quad} $

Question

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": [ "Inscribed Quadrilaterals", "Cyclic Quadrilateral Theorem", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Inscribed Quadrilaterals", "Cyclic Quadrilateral Theorem", "Linear Equations" ] } ## Identify the geometric properties of the inscribed quadrilateral Using the *Inscribed Quadrilaterals* and *Cyclic Quadrilateral Theorem* knowledge points $$ \begin{aligned} &\text{Quadrilateral } FGHJ \text{ is inscribed in the circle.}\ &\angle F \text{ and } \angle H \text{ are opposite angles.}\ &m\angle F + m\angle H = 180^\circ \end{aligned} $$ ## Set up the equation for the opposite angles Using the *Linear Equations* knowledge point $$ \begin{aligned} &(4x + 2) + (9x - 3) = 180 \end{aligned} $$ ## Solve the linear equation for x Using the *Linear Equations* knowledge point $$ \begin{aligned} 13x - 1 &= 180\ 13x &= 181\ x &= \frac{181}{13} \end{aligned} $$ Solve for x: $x =$ $\frac{181}{13}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Cyclic Quadrilateral Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric properties of the inscribed quadrilateral

Set up the equation for the opposite angles

Solve the linear equation for x

Answer: