use the regular pentagon to answer the questions.

what is the sum of the measures of the interior angles?

what is the measure of one interior angle?

what is the sum of the measures of the exterior angles?

what is the measure of one exterior angle?

Question

use the regular pentagon to answer the questions.

what is the sum of the measures of the interior angles?

what is the measure of one interior angle?

what is the sum of the measures of the exterior angles?

what is the measure of one exterior angle?

Accepted Answer

{ "quality": "clear", "question_count": 4, "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 measures of the interior angles $$ \begin{aligned} n &= 5 \ S_{\text{int}} &= (n - 2) \times 180^\circ \ S_{\text{int}} &= (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ \end{aligned} $$ ## Calculate the measure of one interior angle $$ \begin{aligned} \theta_{\text{int}} &= \frac{S_{\text{int}}}{n} \ \theta_{\text{int}} &= \frac{540^\circ}{5} = 108^\circ \end{aligned} $$ ## Determine the sum and measure of the exterior angles $$ \begin{aligned} S_{\text{ext}} &= 360^\circ \ \theta_{\text{ext}} &= \frac{360^\circ}{5} = 72^\circ \end{aligned} $$ ## Question 1 What is the sum of the measures of the interior angles? 540$^\circ$ ## Question 2 What is the measure of one interior angle? 108$^\circ$ ## Question 3 What is the sum of the measures of the exterior angles? 360$^\circ$ ## Question 4 What is the measure of one exterior angle? 72$^\circ$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Polygon Angle Sum Theorem" ] }

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Question

Explanation:

Calculate the sum of the measures of the interior angles

Calculate the measure of one interior angle

Determine the sum and measure of the exterior angles

Answer:

Question 1

Question 2

Question 3

Question 4