Question 1: Calculate the exterior angle of a regular pentagon.

Answer: 72

Question 2: A hexagon has exterior angles of 60°, 75°, 80°, 70°, and 65°. What is the measure of the missing exterior angle?

Answer: 110

Question 3: Explain why the sum of all exterior angles in any polygon is always 360°, regardless of the number of sides.

Answer: Because as you turn around the polygon, the total amount of turning sums to a full rotation of 360°, irrespective of the number of sides.

Question 4: Construct a triangle with exterior angles measuring 100°, 120°, and the remaining exterior angle. Use the grid to draw and verify.

Answer: 140

Question 5: A regular octagon has an exterior angle of:

Answer: 45

Question 6: Identify and correct the mistake: A student claims that the sum of exterior angles in a non-regular polygon can be more or less than 360°. Is this correct? Explain.

Answer: No, the sum of exterior angles in any polygon is always 360°, regardless of regularity.

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

Answer: 51.43

Question 8: A polygon has exterior angles measuring 90°, 60°, 80°, and one more angle. Find the measure of this missing exterior angle.

Answer: 130

Question 9: In a real-world scenario, a carroundabout has 4 exits evenly spaced. What is the measure of the exterior angle between each exit?

Answer: 90

Question 10: A polygon is drawn with exterior angles of 30°, 40°, 50°, and 60°. What is the measure of the fifth exterior angle if the sum must be 360°?

Answer: 180

Question 11: Describe a common mistake students make when calculating exterior angles and how to avoid it.

Answer: Students sometimes add all angles without considering that the sum of exterior angles is always 360°. To avoid this, remember that the exterior angles around a polygon always sum to 360°.