Question 1: Calculate the sum of interior angles of a pentagon.

Answer: 540

Question 2: A hexagon has interior angles that each measure 120°. Calculate the total sum of all interior angles.

Answer: 720

Question 3: Find the number of sides of a polygon if the sum of its interior angles is 1440°.

Answer: 8

Question 4: Construct a polygon with 7 sides and label its interior angles. Use the grid for accuracy.

Answer: Students will draw a heptagon, with each interior angle measuring approximately 128.57°.

Question 5: A regular octagon has an interior angle of 135°. Is this possible? Justify your answer.

Answer: No, because the interior angle of a regular octagon is (n-2)×180°/n=135°, which confirms n=8, and the sum is 1080°, so each angle should be 135°; thus, it's possible.

Question 6: A polygon has 12 sides. Calculate the measure of each interior angle if the polygon is regular.

Answer: 150

Question 7: A polygon's interior angles sum to 1980°. How many sides does the polygon have?

Answer: 15

Question 8: Explain why the sum formula (n-2)×180° works for any polygon, including irregular ones.

Answer: The formula works because any polygon can be divided into (n-2) triangles, each with a sum of 180°, and the total interior angles sum is the sum of these triangles.

Question 9: A decagon has a total interior angle sum of 1440°. What is the measure of each interior angle if the decagon is regular?

Answer: 144

Question 10: A student incorrectly calculates the interior angle sum of a 9-sided polygon as 1620°. Identify and correct the mistake.

Answer: The correct sum is (9-2)×180°=7×180°=1260°, so the student's calculation overestimates the sum by 360°.