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

Answer: 60

Question 2: A pentagon has exterior angles of 70°, 80°, 60°, and 50°. Find the measure of the missing exterior angle.

Answer: 100

Question 3: What is the sum of the exterior angles of any convex polygon?

Answer: 360

Question 4: Construct an octagon where each exterior angle is equal. Calculate the measure of each exterior angle.

Answer: 45

Question 5: A regular heptagon has all its exterior angles equal. If one exterior angle is 50°, what are the measures of all exterior angles? Are these correct? Why or why not?

Answer: Yes, each is 50°, total sum is 350°, which is incorrect because sum must be 360°. Correct measure: approximately 51.43°.

Question 6: Identify and correct the mistake in this reasoning: 'Since the exterior angles of a square are each 90°, their sum is 360°, so any polygon with angles of 90° must have exterior angles summing to 360°.'

Answer: Incorrect because not all polygons with right angles are quadrilaterals; exterior angles depend on the shape. The sum of exterior angles of any convex polygon is always 360°, regardless of the interior angles.

Question 7: A non-convex polygon has an exterior angle of 270°. Why is this possible? What does it tell you about the polygon?

Answer: Because exterior angles can be reflex (more than 180°) in non-convex polygons; total sum still adds to 360° when considering all exterior angles.

Question 8: A polygon has five sides with exterior angles measuring 70°, 72°, 73°, 75°, and an unknown angle. Find the measure of the unknown exterior angle.

Answer: 140

Question 9: Explain why the sum of exterior angles of any convex polygon must be 360°, including a brief reasoning.

Answer: Because as you complete a full turn around the polygon, the exterior angles sum to a full 360°, regardless of the number of sides.

Question 10: A student calculated the sum of exterior angles of a dodecagon as 720°. Identify and explain the error.

Answer: The student doubled the correct sum. The sum of exterior angles of any convex polygon is always 360°, not more.

Question 11: Construct a polygon with sides measuring 4cm, 6cm, 8cm, and 10cm. Without measuring angles, explain whether the exterior angles could sum to 360°, and justify your reasoning.

Answer: Exterior angles depend on the shape, not just side lengths. For a convex polygon, the sum will always be 360°, regardless of side lengths.

Question 12: If a polygon has exterior angles measuring 30°, 50°, 60°, 70°, and 80°, what is the measure of the sixth exterior angle?

Answer: 70