enter answers using commas, if appropriate.

what is the sum of the measures of the interior angles of a 15-gon?

what is the measure of one interior angle of a regular 15-gon?

what is the sum of the exterior angles?

what is the measure of one exterior angle of a regular 15-gon?

Question

enter answers using commas, if appropriate.

what is the sum of the measures of the interior angles of a 15-gon?

what is the measure of one interior angle of a regular 15-gon?

what is the sum of the exterior angles?

what is the measure of one exterior angle of a regular 15-gon?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polygon Angle Sum Theorem", "Interior Angles of a Polygon", "Exterior Angles of Polygons" ], "new_concepts": [], "current_concepts": [ "Polygon Angle Sum Theorem", "Interior Angles of a Polygon", "Exterior Angles of Polygons" ] } ## Calculate the sum of the interior angles of a 15-gon $$ \begin{aligned} S_{\text{int}} &= (n - 2) \times 180^{\circ} \ &= (15 - 2) \times 180^{\circ} \ &= 13 \times 180^{\circ} \ &= 2340^{\circ} \end{aligned} $$ ## Calculate the measure of one interior angle of a regular 15-gon $$ \begin{aligned} A_{\text{int}} &= \frac{S_{\text{int}}}{n} \ &= \frac{2340^{\circ}}{15} \ &= 156^{\circ} \end{aligned} $$ ## Determine the sum of the exterior angles and the measure of one exterior angle $$ \begin{aligned} S_{\text{ext}} &= 360^{\circ} \ A_{\text{ext}} &= \frac{360^{\circ}}{15} = 24^{\circ} \end{aligned} $$ * What is the sum of the measures of the interior angles of a 15-gon? **2,340** * What is the measure of one interior angle of a regular 15-gon? **156** * What is the sum of the exterior angles? **360** * What is the measure of one exterior angle of a regular 15-gon? **24** { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Polygon Angle Sum Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the sum of the interior angles of a 15-gon

Calculate the measure of one interior angle of a regular 15-gon

Determine the sum of the exterior angles and the measure of one exterior angle

Answer: