Question 1: Calculate the measure of angle A when two parallel lines are cut by a transversal and the alternate interior angles are 65 degrees.

Answer: 65

Question 2: Construct a pair of parallel lines on your grid and mark an transversal crossing both. Measure and record the corresponding angles.

Answer: Angles are equal

Question 3: If a chef's recipe calls for doubling the amount of a spice when two lines are parallel, and the original amount is 3 grams, what is the new amount?

Answer: 6

Question 4: Plot on your grid a pair of parallel lines with a transversal creating angles of 120° and 60°. Identify these angles.

Answer: Corresponding angles are 120° and 60°; alternate interior angles are 60° and 120°

Question 1: A baker arranges two parallel shelves for storing baking trays. A rod crosses both shelves, creating angles of 75° and 105°. Explain how the angles relate if the shelves are parallel.

Answer: Since the shelves are parallel and cut by a transversal, the angles of 75° and 105° are supplementary (add up to 180°), and corresponding or alternate interior angles are equal.

Question 2: A chef’s recipe uses a special spice measured in a way that relates to the angles formed by two parallel lines. If the angles are 45° and 135°, and the lines are cut by a transversal, what type of angles are these?

Answer: Supplementary angles

Question 3: On your grid, draw two parallel lines with a transversal such that alternate interior angles are 50°. What are the measures of the corresponding angles?

Answer: 50° for corresponding angles

Question 4: Explain why two parallel lines cut by a transversal always form equal alternate interior angles.

Answer: Because of the properties of parallel lines and transversals, alternate interior angles are equal by the Corresponding Angles Postulate.

Question 1: A recipe book has a diagram showing two parallel counters in a kitchen with a rod crossing both at an angle. If the angle between the rod and the counter is 70°, what is the angle on the opposite side of the rod?

Answer: 70°

Question 2: A chef arranges two parallel shelves with a cutting board crossing both. If the angles at the crossing points are 85° and 95°, explain how this shows the shelves are parallel.

Answer: Angles of 85° and 95° are supplementary and corresponding angles are equal; this confirms the shelves are parallel.

Question 3: In a recipe illustration, a rod crosses two parallel lines (counter and shelf). The angles formed are marked as 60° and 120°. What does this tell about the angles and the lines?

Answer: Angles of 60° and 120° are supplementary, confirming the lines are parallel and the angles are either corresponding or alternate interior.

Question 1: Construct two parallel lines on your grid and draw a transversal such that one of the angles is 130°. Calculate all other angles formed and justify your answers.

Answer: Vertical angles are 130°, alternate interior angles are 130°, and supplementary angles are 50°.

Question 2: A recipe involves arranging multiple parallel lines with a transversal. If one angle is 115°, what are all the other angles, and why?

Answer: Other angles are 115° (alternate interior and corresponding), and 65° (vertical and supplementary).

Question 1: Draw two parallel lines and a transversal. Mark all pairs of corresponding and alternate interior angles, labeling their measures.

Answer: Corresponding angles are equal; alternate interior angles are equal.

Question 2: Identify and correct the mistake in this reasoning: 'Since the angles are 80° and 100°, the lines are not parallel.'

Answer: Angles of 80° and 100° are supplementary, which suggests the lines are not parallel if they are consecutive interior angles.

Question 1: A student states: 'If two lines are parallel, then all angles formed are 90°.' Identify the mistake and explain the correct property.

Answer: The mistake is assuming all angles are 90°. The correct property is that angles formed by a transversal with parallel lines include equal alternate interior, corresponding, and supplementary angles, but they are not all 90°.