find x in this isosceles trapezoid.

an isosceles trapezoid is shown with base angles labeled $(3x + 9)^\circ$ and $(x + 51)^\circ$.

$x = ? $

Question

find x in this isosceles trapezoid.

an isosceles trapezoid is shown with base angles labeled $(3x + 9)^\circ$ and $(x + 51)^\circ$.

$x =  ? $

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": [ "Linear Equations" ], "new_concepts": [ "Isosceles Trapezoid Properties", "Base Angles Theorem" ], "current_concepts": [ "Isosceles Trapezoid Properties", "Base Angles Theorem", "Linear Equations" ] } ## Identify properties of the trapezoid An isosceles trapezoid has congruent base angles. The two base angles shown are $(3x + 9)^\circ$ and $(x + 51)^\circ$. ## Set up the equation Using the **Isosceles Trapezoid Properties** knowledge point, we equate the base angles: $$3x + 9 = x + 51$$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} 3x - x &= 51 - 9\ 2x &= 42\ x &= 21 \end{aligned} $$ Find x in this isosceles trapezoid. $x =$ 21 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Isosceles Trapezoid Properties" ] }

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Question

Explanation:

Identify properties of the trapezoid

Set up the equation

Solve for x

Answer: