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

Answer: 540

Question 2: What is the measure of each interior angle in a regular pentagon?

Answer: 108

Question 3: Construct a regular pentagon with a side length of 5 cm on the grid. (Sketch your construction.)

Answer:

Question 4: Calculate the length of the diagonal in a regular pentagon with side length 6 cm.

Answer: 6.88

Question 1: A pentagon has interior angles measuring 120°, 108°, 108°, 108°, and an unknown angle. Find the measure of the unknown angle.

Answer: 108

Question 2: Explain why the sum of the exterior angles of any convex pentagon is always 360°.

Answer: Because each exterior angle supplements the interior angle and the sum of all exterior angles in any convex polygon is 360°, regardless of the number of sides.

Question 3: A regular pentagon is inscribed in a circle. Calculate the measure of the central angle between two adjacent vertices.

Answer: 72

Question 4: Construct a pentagon with sides of 4 cm each. Then, construct its diagonals. Verify if the diagonals bisect each other.

Answer:

Question 5: Given a pentagon where one interior angle is 135°, and the other four angles are equal, find the measure of each of the other four angles.

Answer: 105

Question 1: A park is designed in the shape of a regular pentagon. Each side is 50 meters. Calculate the total fencing needed around the park.

Answer: 250

Question 2: A tile pattern uses regular pentagonal tiles. If each tile has a side length of 3 inches, what is the approximate area of one tile?

Answer: 11.7

Question 1: Construct a pentagon where the length of each side is twice its apothem. Explain the reasoning behind your construction.

Answer: Students should demonstrate understanding of the relationship between side length and apothem in regular polygons, constructing accordingly.

Question 2: Find the area of a regular pentagon with side length 10 cm, using the apothem method.

Answer: 172.05

Question 1: List all the properties of a regular pentagon.

Answer: Equal sides, equal interior angles (108°), symmetry, diagonals intersect at the center, sum of interior angles 540°, exterior angles 72° each.

Question 2: A student mistakenly calculates the sum of interior angles of a pentagon as 720°. Identify and explain the error.

Answer: Incorrectly adding 180° for each angle instead of summing all angles; correct sum is 540°.

Question 1: A learner calculates each interior angle of a regular pentagon as 90°. Explain why this is incorrect and what the correct measure should be.

Answer: Incorrect because the interior angles of a pentagon are each 108°, not 90°. The sum of interior angles is 540°, so each angle in a regular pentagon is 108°.