Answer:
- agree - the central angle is 360°/n
- agree - a hexagon has 6 degrees of rotational symmetry
- agree - the altitude is r×cos(180°/n)
Explanation:
a)
Agree. All radii of a circle are the same length, so any triangle drawn from the center of a circle to points on the circle will be an isosceles triangle. By definition, all interior angles and all side lengths of a regular polygon are congruent. So, an n-sided regular polygon inscribed in a circle can be divided into n non-overlapping congruent isosceles triangles. That means the central angle is 360°/n, a value found based on the rotational symmetry of the figure.
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b)
Agree. See the explanation in part (a). A regular hexagon has six congruent sides. Each of those can form the base of an isosceles triangle. Hence, the hexagon can be decomposed into 6 congruent isosceles triangles.
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c)
Agree. The altitude divides each of the isosceles triangles of parts (a) and (b) into two congruent right triangles. The length of the altitude can be found as the product of the radius of the circle and the cosine of half the central angle of the isosceles triangle. That is, trigonometry can be used to find the altitude.
The altitude (apothem of the polygon) is ...
a = r·cos(180°/n)
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Additional comment
A "correct" explanation is one that makes sense to you and your grader. The explanation you read here may not be "correct" in that sense. YMMV