point a is the incenter of $\delta def$.

what is the value of $n$?

7
11
14
15

Question

point a is the incenter of $\delta def$.

what is the value of $n$?

7
11
14
15

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", "Linear Equations" ] } ## Identify the properties of the incenter $$ \begin{aligned} &\text{Point } A \text{ is the incenter of } \Delta DEF.\ &\text{Therefore, segment } AD \text{ is the angle bisector of } \angle EDF.\ &\angle EDA = \angle FDA \end{aligned} $$ ## Set up the equation using the given angle measures $$ \begin{aligned} &27^\circ = (3n - 6)^\circ\ &3n - 6 = 27 \end{aligned} $$ ## Solve for n $$ \begin{aligned} &3n = 33\ &n = 11 \end{aligned} $$

7

11

14

15

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

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QUESTION IMAGE

Question

Explanation:

Identify the properties of the incenter

Set up the equation using the given angle measures

Solve for n

Answer: