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

Answer: 540

Question 2: Find the number of sides of a polygon if the sum of its interior angles is 1440°.

Answer: 8

Question 3: What is the measure of each interior angle in a regular octagon?

Answer: 135

Question 4: Construct a polygon with 7 sides and a total interior angle sum of 900°. Use the grid to sketch your polygon.

Answer: A heptagon with each interior angle of approximately 128.57°

Question 5: A polygon has 12 sides. Calculate the measure of each interior angle if the polygon is regular.

Answer: 150

Question 6: Explain why the sum of interior angles of a triangle is 180° using the sum formula.

Answer: For a triangle, n=3. (n-2)×180° = (3-2)×180°=180°, which explains the total sum.

Question 7: A hexagon has one interior angle measuring 120°. If the remaining five angles are equal, find the measure of each of these angles.

Answer: 144

Question 8: Determine the number of sides of a polygon if each interior angle is 143° and the polygon is regular.

Answer: 25

Question 9: A polygon has 9 sides. Calculate the sum of all its interior angles.

Answer: 1260

Question 10: Common mistake: A student calculates the sum for a pentagon as 720°. Identify and correct this mistake.

Answer: Incorrect. For a pentagon, n=5, so sum = (5-2)×180°=3×180°=540°.

Question 11: Challenge: A polygon has 15 sides. The measure of each interior angle in a regular form is increased by 10° from the standard value. Find the new measure of each angle.

Answer: 160