Question 1: Calculate the sum of the interior angles of a hexagon.

Answer: 720

Question 2: What is the measure of each interior angle in a regular hexagon?

Answer: 120

Question 3: Calculate the measure of each exterior angle in a regular hexagon.

Answer: 60

Question 4: Construct a regular hexagon on the grid with side length 4 units. Label all sides.

Answer: Construction on grid; no numerical answer.

Question 5: A hexagon has interior angles of 125°, 125°, 130°, 125°, 125°, and an unknown angle. Find the measure of the unknown angle.

Answer: 120

Question 6: Calculate the length of the diagonal in a regular hexagon with side length 6 units.

Answer: 6√3 ≈ 10.39

Question 7: A hexagon has sides of lengths 5, 7, 5, 7, 5, 7 units. Is it regular? Explain your reasoning.

Answer: No, because the sides are not all equal.

Question 8: In a real-world scenario, a hexagonal tile has a side length of 3 inches. How many such tiles would be needed to cover a rectangular area measuring 18 inches by 24 inches, assuming perfect tiling without gaps?

Answer: 36 tiles

Question 9: Identify the common mistake: A student calculates interior angles of a hexagon as 130° each and concludes the total sum is 780°. Explain the error and correct it.

Answer: Students forgot to sum all angles or incorrectly divided 720° by 6; total sum is 720°, each interior angle in a regular hexagon is 120°.

Question 10: A hexagon is stretched so that one interior angle increases by 10°, and another decreases by 10°, keeping the total sum of interior angles unchanged. If originally all angles were equal, what are the new angles?

Answer: One angle is 130°, another is 110°, others remain 120°.

Question 11: Determine whether a hexagon with sides 4, 4, 4, 4, 4, 4 units is necessarily convex. Justify your answer.

Answer: Yes, all sides equal and angles less than 180° ensure convexity.