tangent lines

what is the value of $x$?

$x = \quad^{\circ}$

Question

tangent lines

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", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Angles Outside Circle Theorem" ], "new_concepts": [ "Tangent-Tangent Angle", "Central Angle Theorem" ], "current_concepts": [ "Angles Outside Circle Theorem", "Tangent-Tangent Angle", "Central Angle Theorem" ] } ## Identify the properties of the triangle Using the *Angles Outside Circle Theorem* knowledge point $$ \begin{aligned} &\text{The two segments from the center to the points of tangency are radii.}\ &\text{The chord connecting the two points of tangency forms a triangle with the radii.}\ &\text{Since all radii of a circle are equal, the triangle is equilateral (indicated by the tick marks).}\ &\text{Therefore, the central angle is } 60^\circ. \end{aligned} $$ ## Calculate the value of x Using the *Angles Outside Circle Theorem* knowledge point $$ \begin{aligned} &\text{The angle between two tangents meeting outside a circle is supplementary to the central angle.}\ &x^\circ + 60^\circ = 180^\circ\ &x = 120 \end{aligned} $$ What is the value of x? $x =$ 120$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Angles Outside Circle Theorem" ] }

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Question

Explanation:

Identify the properties of the triangle

Calculate the value of x

Answer: