Question 1: In the diagram, two parallel lines are cut by a transversal. If one of the corresponding angles measures 65°, find the measures of the other three corresponding angles.

Answer: 65

Question 2: Calculate the value of angle x if the corresponding angle to a 110° angle is in the same position in the F-pattern.

Answer: 110

Question 3: Construct a pair of parallel lines cut by a transversal such that one of the corresponding angles is 75°. Use the grid to accurately draw the lines and indicate the angles.

Answer: Correctly drawn lines with marked 75° angles

Question 4: Identify the error in this reasoning: 'Since the angles are in an F-pattern, all corresponding angles are equal, so if one is 90°, all are 90°.'

Answer: Incorrect because only pairs of corresponding angles are equal, not all angles in the pattern

Question 5: A transversal cuts two parallel lines, creating an F-pattern. If one corresponding angle is 120°, what is the measure of the alternate interior angle on the same side?

Answer: 120

Question 6: In a real-world scenario, a fence post is aligned parallel to a lamp post. The angle between the fence and the line of sight from a point 10 meters away is 70°. If the line of sight is extended to meet the parallel fence, what is the angle of elevation to the top of the fence assuming the same F-pattern applies?

Answer: 70°

Question 7: Prove that the corresponding angles are equal using the properties of parallel lines and transversals.

Answer: Using the Alternate Interior Angles Theorem

Question 8: Using the grid, construct two parallel lines cut by a transversal such that one of the corresponding angles measures 85°. Mark all angles involved.

Answer: Correctly constructed lines with marked 85° angles

Question 9: What is the measure of the angle supplementary to a 125° corresponding angle in the F-pattern?

Answer: 55

Question 10: A challenging problem: Two parallel lines are cut by a transversal, forming an F-pattern. If an angle in the pattern is unknown, but adjacent to a 60° angle, and the alternate interior angle is 120°, find the unknown angle.

Answer: 60

Question 11: Explain how the F-pattern helps you determine unknown angles in complex diagrams involving parallel lines and transversals.

Answer: It shows the correspondence between angles, allowing logical deduction of unknowns based on known angles in the pattern.