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": [ "Tangent-Tangent Angle" ], "new_concepts": [], "current_concepts": [ "Tangent-Tangent Angle", "Central Angle Theorem", "Tangent-Radius Theorem" ] } ## Identify the geometric relationship $$ \text{Angle formed by two tangents} + \text{Central angle intercepting the same minor arc} = 180^\circ $$ ## Set up the equation $$ 26^\circ + x^\circ = 180^\circ $$ ## Solve for x $$ x = 180 - 26 = 154 $$ What is the value of x? $x =$ 154$^\circ$ { "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 geometric relationship

Set up the equation

Solve for x

Answer: