Concave & Convex polygon

Select the definition of a convex polygon.

• A polygon is convex if it contains one or more interior angles greater than 180∘

• A polygon is convex if it all interior angles are less than 180∘.

• A polygon is convex if it contains one or more interior angles less than 180∘.

• A polygon is convex if some of its vertices point “inward,” toward the center.

In a pentagon 𝐴𝐵𝐶𝐷𝐸,𝑚∠𝐴=110∘,𝑚∠𝐷=62∘,𝑚∠𝐸=89∘,and 𝑚∠𝐵=𝑚∠𝐶.

Decide whether 𝐴𝐵𝐶𝐷𝐸 is convex or concave.

• The given information is not enough.

• convex

• concave

Answer explanation

Based on the information, we can see that angle B and C are both 139.5^。. All interior angles are less than 180^。, so it's a convex polygon.

Which of the following polygons is not a concave polygon?

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Determine the type of the polygon, and classify if it's regular/irregular, and if it's convex/concave.

• Irregular concave pentagon

• irregular convex pentagon

• regular concave hexagon

• regular convex pentagon

Determine the type of the polygon, and classify if it's regular/irregular, and if it's convex/concave.

• irregular convex hexagon

• irregular concave hexagon

• regular convex hexagon

• regular concave hexagon

Which of the following shape is convex polygon? Choose all that apply.

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Classify if the polygon is regular/irregular, convex/concave, type of polygon.

The polygon is a ​​ (a)   ​ (b)   ​ (c)  

• irregular
• convex
• quadrilateral
• square
• regular
• concave

Classify the type of polygon, if it's irregular/regular and concave/convex.

• Hexagon irregular concave

• Heptagon irregular convex

• Hexagon irregular convex

• Octagon irregular concave

Which of these properties is true of a concave polygon?

• All of its internal angles are 180 degrees at most.

• All the vertices are pointing outward.

• One or more of its internal angles are more than 180 degrees.

• All its internal angles are more than 180 degrees.