Question 1: Calculate the measure of each exterior angle of a regular hexagon.

Answer: 60

Question 2: A polygon has 5 sides. If one exterior angle measures 72°, what is the total of the other exterior angles?

Answer: 288

Question 3: In a regular octagon, what is the measure of each exterior angle? Show your working.

Answer: 45

Question 4: A pentagon has exterior angles that sum to 360°. If four of the exterior angles are 70°, 80°, 60°, and 50°, what is the measure of the fifth exterior angle?

Answer: 100

Question 5: True or False: The sum of the exterior angles of any polygon is always 360°, regardless of the number of sides.

Answer: True

Question 6: Construct a triangle with exterior angles measuring 100°, 80°, and the remaining angle. Calculate the third exterior angle.

Answer: 180

Question 7: A regular decagon has exterior angles. What is the measure of each exterior angle? Show your working.

Answer: 36

Question 8: A car turns at an intersection forming an exterior angle of 45°. If the turn is part of a regular polygon path, how many sides does this polygon have?

Answer: 8

Question 9: In a real-world scenario, a square garden is surrounded by a path making exterior angles of 90°. Confirm that the sum of these exterior angles is 360° and explain why this makes sense in context.

Answer: The sum of the exterior angles of a square is 360°, which means the full turn around the garden is 360°, consistent with the property that exterior angles of any polygon sum to 360°.

Question 10: A polygon has exterior angles of 50°, 60°, 70°, 80°, and the remaining angles are equal. Find the measure of each of the remaining angles.

Answer: 100

Question 11: Identify a common mistake students might make when calculating the exterior angles of a polygon and explain how to correct it.

Answer: A common mistake is to add all exterior angles without realizing they should sum to 360°, or to assume each exterior angle is equal when the polygon is irregular. To correct this, remember that the total sum of exterior angles for any polygon is 360° and check each angle accordingly.