Question 1: Calculate the measure of angle x if it is co-interior with a 120° angle on a parallel line.

Answer: 60

Question 2: On two parallel lines cut by a transversal, one co-interior angle measures 75°. What is the measure of its adjacent co-interior angle?

Answer: 105

Question 3: Construct a pair of parallel lines with a transversal so that the co-interior angles are 110° and x°. Calculate the value of x.

Answer: 70

Question 4: If two co-interior angles on parallel lines are 130° and y°, what is the value of y?

Answer: 50

Question 5: A pair of parallel lines are cut by a transversal. The sum of two co-interior angles is 180°. If one angle is 85°, what is the measure of the other?

Answer: 95

Question 6: In a real-world scenario, a road is parallel to a canal. The angles of elevation from a point on the road to a bridge are 110° and 70° at two different points. Explain why these angles are co-interior and verify that they sum to 180°.

Answer: Because the angles are on the same side of the transversal (the line of sight) and between the parallel lines (the road and canal), they are co-interior and should sum to 180°. 110° + 70° = 180°.

Question 7: A diagram shows two parallel lines cut by a transversal, with one co-interior angle marked as 95°. Find the measure of the adjacent co-interior angle.

Answer: 85

Question 8: Two co-interior angles are 60° and 120°. Are the lines parallel? Justify your answer.

Answer: Since the angles are not supplementary (they do not sum to 180°), the lines are not parallel.

Question 9: A teacher draws two parallel lines and a transversal. The angles formed are 45° and x°. What is the value of x?

Answer: 135

Question 10: Challenge Question: Two parallel lines are cut by a transversal, forming a pair of co-interior angles. If one angle is (3x + 20)° and the other is (2x + 80)°, find x and the angles.

Answer: x=20, angles=80° and 120°

Question 11: Identify and correct the mistake in the following statement: 'Co-interior angles on parallel lines are always equal.'

Answer: The mistake is that co-interior angles on parallel lines are always supplementary, not equal. They sum to 180°, but are not necessarily equal.