find the value of $x$ in the triangle shown below.

$x = \boxed{\phantom{123}}^{\circ}$

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Question

find the value of $x$ in the triangle shown below.

$x = \boxed{\phantom{123}}^{\circ}$

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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": [], "new_concepts": [ "Isosceles Triangle Theorem", "Base Angle Theorem" ], "current_concepts": [ "Isosceles Triangle Theorem", "Base Angle Theorem", "Triangle Angle Sum Theorem" ] } ## Identify the triangle type $$ \text{Side lengths: } a = 6, \quad b = 6, \quad c = 5.8 $$ $$ \text{Since two sides are equal } (6 = 6)\text{, the triangle is isosceles.} $$ ## Apply the Isosceles Triangle Theorem $$ \text{The angles opposite to the equal sides of length } 6 \text{ must be equal.} $$ $$ \text{Angle opposite to side of length } 6 \text{ is } 58^\circ. $$ $$ \text{Angle opposite to the other side of length } 6 \text{ is } x^\circ. $$ $$ x = 58 $$ Find the value of $x$ in the triangle shown below. $x =$ 58$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Isosceles Triangle Theorem" ] }

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Question

Explanation:

Identify the triangle type

Apply the Isosceles Triangle Theorem

Answer: