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

Answer: 45

Question 2: A regular polygon has an exterior angle of 30°. How many sides does this polygon have?

Answer: 12

Question 3: Find the measure of each exterior angle of a regular decagon.

Answer: 36

Question 4: Construct a triangle with one exterior angle measuring 120° and the other two angles equal. Show your working.

Answer: Each of the other two exterior angles measures 60°, corresponding to interior angles of 120°.

Question 5: A pentagon has exterior angles as follows: 72°, 72°, 72°, 72°, and an unknown angle. Find the unknown exterior angle.

Answer: 72

Question 6: Explain why the sum of all exterior angles in any polygon is always 360°. Use reasoning in your answer.

Answer: Because as you go around the polygon, each exterior angle turns you through a full circle (360°), regardless of the number of sides.

Question 7: A regular nonagon (9 sides) has an exterior angle of what measure?

Answer: 40

Question 8: A shape has four exterior angles measuring 80°, 85°, 90°, and an unknown angle. Find the measure of the unknown exterior angle.

Answer: 105

Question 9: A polygon's three exterior angles are 50°, 70°, and 90°. What is the measure of its fourth exterior angle?

Answer: 150

Question 10: A polygon has 8 sides. What is the measure of each exterior angle?

Answer: 45

Question 11: Identify and correct the mistake in this reasoning: 'Since the sum of exterior angles of any polygon is 360°, if one exterior angle is 45°, then the polygon has 8 sides.'

Answer: Misconception: The exterior angles of a polygon are not all equal unless it is regular; also, knowing one exterior angle does not determine the number of sides unless all are equal.