each exterior angle of a regular octagon measures:
select one:
a. $36^\circ$
b. $40^\circ$
c. $30^\circ$
d. $45^\circ$

the interior angles of a regular polygon each measure $135^\circ$. how many sides does the polygon have?
select one:
a. 12
b. 8
c. 10
d. 6

a polygon has an interior angle sum of $1080^\circ$. how many sides does it have?
select one:
a. 6
b. 7
c. 8
d. 9

Question

each exterior angle of a regular octagon measures:
select one:
a. $36^\circ$
b. $40^\circ$
c. $30^\circ$
d. $45^\circ$

the interior angles of a regular polygon each measure $135^\circ$. how many sides does the polygon have?
select one:
a. 12
b. 8
c. 10
d. 6

a polygon has an interior angle sum of $1080^\circ$. how many sides does it have?
select one:
a. 6
b. 7
c. 8
d. 9

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Regular Polygon Properties", "Polygon Classification" ], "new_concepts": [ "Polygon Interior Angle Sum", "Polygon Exterior Angle Formula" ], "current_concepts": [ "Regular Polygon Properties", "Polygon Classification", "Polygon Interior Angle Sum", "Polygon Exterior Angle Formula" ] } ## Calculate exterior angle of a regular octagon $$ \begin{aligned} &n = 8\ &\theta_{\text{ext}} = \frac{360^\circ}{n} = \frac{360^\circ}{8} = 45^\circ \end{aligned} $$ ## Find number of sides from interior angle $$ \begin{aligned} &\theta_{\text{int}} = 135^\circ\ &\theta_{\text{ext}} = 180^\circ - 135^\circ = 45^\circ\ &n = \frac{360^\circ}{\theta_{\text{ext}}} = \frac{360^\circ}{45^\circ} = 8 \end{aligned} $$ ## Find number of sides from interior angle sum $$ \begin{aligned} &S = (n - 2) \times 180^\circ = 1080^\circ\ &n - 2 = \frac{1080^\circ}{180^\circ} = 6\ &n = 8 \end{aligned} $$ ## Question 1 a. $36^\circ$

b. $40^\circ$

c. $30^\circ$

d. $45^\circ$ ## Question 2 a. 12

b. 8

c. 10

d. 6 ## Question 3 a. 6

b. 7

c. 8

d. 9

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Polygon Interior and Exterior Angles" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate exterior angle of a regular octagon

Find number of sides from interior angle

Find number of sides from interior angle sum

Answer:

Question 1

Question 2

Question 3