line segment gj is a diameter of circle l. angle k measures $(4x + 6)^\circ$.

what is the value of $x$?

$\bigcirc$ 21
$\bigcirc$ 24
$\bigcirc$ 32
$\bigcirc$ 44

Question

line segment gj is a diameter of circle l. angle k measures $(4x + 6)^\circ$.

what is the value of $x$?

$\bigcirc$ 21
$\bigcirc$ 24
$\bigcirc$ 32
$\bigcirc$ 44

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Thaless Theorem" ], "new_concepts": [], "current_concepts": [ "Thaless Theorem", "Inscribed Angle Theorem", "Circle Geometry" ] } ## Apply Thales's Theorem to find the angle measure $$ \begin{aligned} &\text{Since } GJ \text{ is a diameter of circle } L, \text{ the inscribed angle } \angle GKJ \text{ is a right angle.}\ &m\angle K = 90^\circ \end{aligned} $$ ## Set up the equation for x $$ \begin{aligned} &4x + 6 = 90 \end{aligned} $$ ## Solve for x $$ \begin{aligned} &4x = 84\ &x = 21 \end{aligned} $$

(A) 21

(B) 24

(C) 32

(D) 44

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Thaless Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Apply Thales's Theorem to find the angle measure

Set up the equation for x

Solve for x

Answer: