point g is the incenter of the triangle
what is the value of x?
4
8
24
32

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Incenter Theorem", "Angle Bisector" ], "current_concepts": [ "Incenter Theorem", "Angle Bisector" ] } ## Apply the definition of an incenter $$ \text{Incenter } G \implies \text{Segment } FG \text{ bisects } \angle DFE $$ ## Set up the angle bisector equation $$ 16^\circ = (2x)^\circ $$ ## Solve for x $$ \begin{aligned} 2x &= 16 \ x &= 8 \end{aligned} $$

(A) 4

(B) 8

(C) 24

(D) 32

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

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QUESTION IMAGE

Question

Explanation:

Apply the definition of an incenter

Set up the angle bisector equation

Solve for x

Answer: