Question 1: Calculate the sum of the interior angles of an octagon.

Answer: 1080

Question 2: A regular octagon has an exterior angle of 45°. Verify this and find the measure of each interior angle.

Answer: Interior angle = 135°

Question 3: Construct a regular octagon with a side length of 5 cm. Describe the steps involved.

Answer: Construct octagon by drawing a circle, dividing into 8 equal arcs, connecting points with chords of length 5cm, ensuring symmetry.

Question 4: In an octagon, one interior angle measures 140°. If the other seven are equal, what is their measure?

Answer: 126°

Question 5: Calculate the length of the diagonal in a regular octagon with side length 6 cm. (Use approximate methods if necessary.)

Answer: Approximately 8.49 cm

Question 6: Determine the measure of the exterior angle of a regular octagon and verify the sum of all exterior angles.

Answer: Exterior angle = 45°, sum = 360°

Question 7: A polygon has interior angles of 135°, 125°, 130°, and 120°. The remaining four angles are equal. Find each of these four angles.

Answer: 126.25°

Question 8: Using geometric construction, draw a non-regular octagon where two sides are longer than the others. Describe your approach.

Answer: Construct octagon with specified side lengths, ensuring angles are adjusted accordingly to maintain octagon shape, using compass and straightedge.

Question 9: A student mistakenly calculates the sum of interior angles of an octagon as 900°. Identify the error and provide the correct total.

Answer: Incorrect summation; the correct total is 1080° because sum of interior angles of any octagon = 180° × (8−2) = 1080°.

Question 10: Challenge: Derive a formula for the area of a regular octagon given side length s, using known geometric methods.

Answer: Area = 2(1 + √2) s²