Question 1: In the diagram, two parallel lines are cut by a transversal. If one of the alternate angles forming the 'Z' pattern measures 65°, find the other alternate angle.

Answer: 65

Question 2: Construct a diagram showing two parallel lines cut by a transversal. Label the alternate angles and mark an angle of 50°. Use the Z-pattern to find the measure of the corresponding alternate angle.

Answer: 50

Question 3: If the Z-pattern angle at point A is 70°, what is the measure of the alternate angle at point B?

Answer: 70

Question 4: Calculate the value of an alternate angle if the corresponding angle in the Z-pattern is 45°.

Answer: 45

Question 5: Explain why alternate angles are congruent when two parallel lines are cut by a transversal, using the Z-pattern as a reference.

Answer: When two parallel lines are cut by a transversal, the Z-pattern shows that alternate angles are equal because corresponding angles are equal and the Z-pattern demonstrates this relationship through the angles formed.

Question 6: In a diagram with parallel lines and a transversal, an alternate angle measures 80°. What are the measures of the other three angles in the Z-pattern?

Answer: 80, 80, 100, 100

Question 7: A pair of parallel lines are cut by a transversal. If the alternate angle is 120°, find the corresponding angles on both lines.

Answer: 120, 120

Question 8: Use the Z-pattern to determine the measure of an unknown angle if one of the alternate angles is 55° and the other known angle is 125°.

Answer: 55

Question 9: Identify and correct the mistake in the following statement: 'Alternate angles are equal, so if one is 60°, the other must be 60° regardless of whether the lines are parallel.'

Answer: The lines must be parallel for the angles to be equal; if the lines are not parallel, the angles may not be equal.

Question 10: Using the Z-pattern, prove that the sum of the two alternate angles is 180° in a diagram with parallel lines.

Answer: The Z-pattern shows that the angles are supplementary because they form a linear pair when extended, summing to 180°.

Question 11: Challenge: Two parallel lines are cut by a transversal. If one alternate angle is x°, and its corresponding angle is 3x°, find the value of x.

Answer: 45

Question 12: Construct a diagram showing parallel lines cut by a transversal, with an angle of 70° in the Z-pattern. Use the diagram to find the measure of the alternate angle.

Answer: 70