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

Answer: 60

Question 2: A pentagon has an exterior angle of 72°. What is the sum of the other four exterior angles?

Answer: 288

Question 3: Construct a quadrilateral with three exterior angles measuring 70°, 85°, and 100°. What is the measure of the fourth exterior angle?

Answer: 105

Question 4: Explain why the sum of exterior angles of any convex polygon always equals 360°.

Answer: Because each exterior angle corresponds to a turn at a vertex and the total turn around a polygon is 360°.

Question 5: A regular octagon has exterior angles of equal measure. What is the size of each exterior angle?

Answer: 45

Question 6: A polygon has five exterior angles: 80°, 75°, 70°, 65°, and ?°. Find the missing exterior angle.

Answer: 70

Question 7: A regular dodecagon (12 sides) has equal exterior angles. Calculate the measure of each exterior angle.

Answer: 30

Question 8: A triangular prism has a base with exterior angles of 60°, 80°, and 100°. Are these angles possible for a triangle? Why or why not?

Answer: No, because the sum of triangle exterior angles should be 360°, but these sum to 240°.

Question 9: Find the exterior angle of a regular decagon.

Answer: 36

Question 10: In a certain polygon, one exterior angle is 40°. If the sum of all exterior angles is 360°, how many sides does the polygon have?

Answer: 9

Question 11: Identify and correct the mistake: A pentagon has exterior angles of 72°, 72°, 72°, 72°, and 102°. Are these angles valid? Why or why not?

Answer: No, because the sum is 340°, not 360°. The angles are invalid.

Question 12: Calculate the measure of each exterior angle of a regular polygon with 15 sides.

Answer: 24