measurement and geometry continued
6. determine the values of angles $x$ and $y$.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Regular Polygon Angles", "Interior and Exterior Angles" ], "current_concepts": [ "Regular Polygon Angles", "Interior and Exterior Angles" ] } ## Calculate the interior angle $y$ of the regular pentagon $$ \begin{aligned} n &= 5 \ y &= \frac{(n - 2) \times 180^\circ}{n} \ y &= \frac{(5 - 2) \times 180^\circ}{5} \ y &= \frac{3 \times 180^\circ}{5} \ y &= 108^\circ \end{aligned} $$ ## Calculate the exterior angle $x$ $$ \begin{aligned} x &= 180^\circ - y \ x &= 180^\circ - 108^\circ \ x &= 72^\circ \end{aligned} $$ $x = 72^\circ$, $y = 108^\circ$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Regular Polygon Angles" ] }

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Explanation:

Calculate the interior angle \(y\) of the regular pentagon

Calculate the exterior angle \(x\)

Answer: