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

Answer: 540

Question 2: In a regular pentagon, each interior angle measures how many degrees?

Answer: 108

Question 3: Construct a pentagon with sides of 5 cm each. Label all sides.

Answer: Constructed diagram with all sides 5 cm

Question 4: Plot the graph of y = 2x and label the point where x = 3. Using the grid, draw a pentagon with one side along this line.

Answer: Graph and pentagon on grid with side along y=6 at x=3

Question 5: Find the measure of the missing interior angle in a pentagon where four angles are 120°, 115°, 105°, and 110°.

Answer: 50

Question 6: A pentagon has interior angles measuring 110°, 108°, 112°, 105°, and one angle is unknown. Find the measure of the unknown angle.

Answer: 65

Question 7: A real estate agent designs a pentagonal garden with sides of 8 meters, 10 meters, and three sides of 6 meters each. The sides are arranged to form a closed shape. Which property of a pentagon allows this shape to be possible, and how would you verify it?

Answer: The property is that side lengths and angles can vary; verification involves checking if the sides can connect to form a closed shape with the given lengths, possibly using construction or coordinate geometry.

Question 8: Identify and correct the mistake in the following statement: 'All pentagons have 540° interior angles, and each angle in a regular pentagon measures 120°.'

Answer: Incorrect because each interior angle in a regular pentagon measures 108°, not 120°.

Question 9: A pentagon has sides measuring 7 cm, 10 cm, 8 cm, 9 cm, and 6 cm. Is it possible to construct such a pentagon? Explain your reasoning.

Answer: Yes, if the sum of any four sides is greater than the fifth side, which is true here, so construction is possible.

Question 10: Calculate the length of the diagonal in a regular pentagon with side length 6 cm.

Answer: Approximately 8.7 cm (using formula or approximation for diagonals in regular pentagons)

Question 11: Challenge: Prove that the sum of the measures of the exterior angles of any convex pentagon is 360°.

Answer: Since each exterior angle is supplementary to the interior angle and the sum of all exterior angles of any convex polygon is always 360°, this holds for a pentagon as well.