Question 1: What is the sum of the interior angles of an octagon?

Answer: 1080

Question 2: Calculate the measure of each interior angle in a regular octagon.

Answer: 135

Question 3: Construct a regular octagon with each side measuring 5 cm on the grid. (Describe the steps or draw the octagon.)

Answer: Constructed octagon with 8 equal sides, each 5cm long, with interior angles of 135°.

Question 4: If one interior angle of a regular octagon measures 140°, is it a regular or irregular octagon? Explain.

Answer: Irregular, because in a regular octagon each interior angle should be 135°.

Question 5: Plot the vertices of a regular octagon with vertices spaced evenly around a circle of radius 4 cm on the grid.

Answer: Vertices evenly spaced at 45° intervals around a circle; draw octagon connecting these points.

Question 6: A polygon has interior angles measuring 135°, 135°, 135°, 135°, 135°, 135°, 135°, and 135°. Is this polygon an octagon? Why or why not?

Answer: Yes, because the sum of interior angles matches that of an octagon and all angles are equal.

Question 7: Calculate the exterior angle of a regular octagon.

Answer: 45

Question 8: Explain why the sum of all exterior angles of any polygon is always 360°.

Answer: Because exterior angles, one at each vertex, form a full circle around the polygon, summing to 360°.

Question 9: A regular octagon is inscribed in a circle. What is the measure of the central angle between two adjacent vertices?

Answer: 45

Question 10: Identify and correct the mistake in the following statement: 'In an octagon, all sides are equal, but the interior angles are different.'

Answer: In a regular octagon, all interior angles are equal; in an irregular octagon, sides or angles may differ.

Question 11: Calculate the length of the diagonal connecting two opposite vertices in a regular octagon with side length 6 cm.

Answer: Diagonal length = 6√2 + 6 ≈ 17.0 cm (approximate)