SOLUTION: Juan cut out a polygon with scissors and card board. All the angles in the polygon were acute. What type of polygon could he have drawn? A. pentagon B. octagon C. triangle (

Question 1203594: Juan cut out a polygon with scissors and card board. All the angles in the polygon were acute. What type of polygon could he have drawn?
A. pentagon
B. octagon
C. triangle (correct answer)
D. hexagon
I need to know how to determine the correct answer.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
A triangle is a basic polygon with three sides and three vertices. Since it has three sides, it has three interior angles. An angle that measures between ° and ° is called an . An acute triangle is a type of triangle in which all the three internal angles of the triangle are acute.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

"acute" means the measure of an angle is less than 90 degrees.

For a triangle, the sum of the angle measures is 180 degrees, so the average of the angle measures is 180/3 = 60 degrees. Since that is less than 90 degrees, the polygon he drew could have been a triangle.

For a quadrilateral, the sum of the angle measures is 360 degrees, so the average of the angle measures is 360/4 = 90 degrees. Since that is not less than 90 degrees, the polygon he drew could not have been a quadrilateral.

For polygons with more than 4 sides, the average of the angle measures is always greater then 90 degrees, so it is not possible that the polygon he drew has more then 4 sides.

ANSWER: triangle

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