unit exam - circles

what is the value of $x$?

$x = \quad^{\circ}$

Question

unit exam - circles

what is the value of $x$?

$x = \quad^{\circ}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Equilateral Triangle Properties", "Tangent-Tangent Angle" ], "new_concepts": [], "current_concepts": [ "Equilateral Triangle Properties", "Tangent-Radius Theorem", "Tangent-Tangent Angle" ] } ## Identify the central angle $$ \text{Triangle is equilateral} \implies \text{Central Angle} = 60^\circ $$ ## Apply the Tangent-Tangent Angle Theorem $$ x^\circ + 60^\circ = 180^\circ $$ ## Solve for x $$ x = 120 $$ What is the value of $x$? $x =$ 120$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Tangent-Tangent Angle" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the central angle

Apply the Tangent-Tangent Angle Theorem

Solve for x

Answer: