Question 1: In the diagram, lines l and m are parallel, and a transversal t cuts both lines forming Z-pattern angles. If one of the alternate interior angles in the Z-pattern measures 65°, what is the measure of the corresponding alternate interior angle?

Answer: 65

Question 2: Construct a diagram where two parallel lines are intersected by a transversal, forming a Z-pattern. Mark one alternate interior angle as 70°. Using the Z-pattern, find the measure of its alternate interior angle.

Answer: 70

Question 3: A pair of parallel lines are cut by a transversal. If one of the Z-pattern angles is 110°, what is the measure of the alternate interior angle on the same side of the transversal?

Answer: 70

Question 4: Plot a pair of parallel lines with a transversal. On your diagram, mark one Z-pattern angle as 50°. Measure and label the alternate interior angle using your grid.

Answer: 50

Question 5: In a real-world scenario, a road (parallel line) is crossed by a bridge (transversal). If a driver sees the angle of elevation as 45°, and this forms part of a Z-pattern with the opposite angle, what is the angle of elevation on the other side?

Answer: 45

Question 6: Two parallel lines are intersected by a transversal. If one Z-pattern angle measures 85°, what is the measure of the angle vertically opposite to it?

Answer: 85

Question 7: Construct a diagram with two parallel lines and a transversal. Mark a Z-pattern angle as 120°. Calculate the measure of its corresponding alternate interior angle.

Answer: 120

Question 8: Identify and fix the mistake in the following reasoning: 'If a Z-pattern angle is 60°, then the alternate interior angle on the same side of the transversal is 120°.'

Answer: Incorrect, alternate interior angles are equal when lines are parallel, so it should also be 60°.

Question 9: A pair of parallel lines are cut by a transversal, forming a Z-pattern. If the sum of the two Z-pattern angles on the same side is 180°, find the measure of each angle if one is 65°.

Answer: 115

Question 10: Challenge: Prove that when two parallel lines are cut by a transversal, the alternate interior angles are equal using the Z-pattern, and explain why this must be true.

Answer: Because in a Z-pattern, the angles are corresponding or alternate interior angles, which are equal when lines are parallel.

Question 11: Mixed Review: Draw two parallel lines and a transversal. Mark three different Z-pattern angles: 40°, 70°, and 110°. Verify which pairs are alternate interior angles and which are corresponding.

Answer: Angles 40° and 110° are not alternate interior; 70° and the other 70° are alternate interior; corresponding angles match if they are equal.