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Each of the following statements is true or false. Which statements are true?

A. A triangle where at least two angles are acute is called an acute triangle.
B. Some polygons are neither convex nor concave.
C. The sum of the interior angles of a concave pentagon is $540^{\circ}.$
D. The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.
E. The exterior angles of a regular $1000$-gon are greater than the exterior angles of a regular $100$-gon.

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Answer:

  A. False

  B. False

  C. True

  D. True

  E. False

Step-by-step explanation:

A. False -- any triangle has at least two acute angles, whether it is acute, right, or obtuse.

B. False -- by definition, any polygon that is not convex is concave.

C. True -- the angle sum is the same regardless of whether the pentagon is convex or concave. (Provided it is a "simple" polygon, with no crossing sides.)

D. True -- the measure of the interior angle of a regular polygon increases as the number of sides increases. (see E)

E. False -- the exterior angles of a regular polygon are 360° divided by the number of sides. As the number of sides increases, the measure of each exterior angle decreases. (Interior angles are the supplement of exterior angles, so they increase as the number of sides increases.)

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