Question 1: In a nature reserve, two parallel fences are crossed by a path. The angle between the fence and the path on one side is 65°. What is the measure of the co-interior angle on the other side of the path?

Answer: 115

Question 2: Calculate the measure of the angle adjacent to a 120° angle on a straight line, assuming the line represents a boundary in a forest area.

Answer: 60

Question 3: Two trees are aligned such that a line from the top of one to the top of the other forms a 70° angle with a horizontal line in a park. If a parallel fence runs nearby, what is the measure of the co-interior angle formed where the fence intersects the line of sight?

Answer: 110

Question 4: A gardener plants parallel rows of trees. The angle between the row and a footpath crossing it is 55°. What is the measure of the co-interior angle on the opposite side of the footpath?

Answer: 125

Question 5: Construct a diagram showing two parallel lines and a transversal where one co-interior angle measures 80°. Label all relevant angles and verify that the sum of the co-interior angles equals 180°.

Answer: Angles sum to 180° as per co-interior angle rule

Question 6: A river flows parallel to a series of channels in a wetland. The angle between the riverbank and a drainage channel at one crossing is 48°. What is the measure of the co-interior angle on the opposite side of the crossing?

Answer: 132

Question 7: In a landscape, two identical hills are viewed through a gap in trees aligned along a straight line. The angle of elevation to the top of the first hill is 40°, and the angle on the other side of the line to the second hill is 140°. Assuming the line of sight forms a pair of co-interior angles with a straight boundary in the environment, find the measure of the angle between the boundary and the line of sight.

Answer: 40

Question 8: A wildlife photographer sets up two parallel fences and a camera on a tripod. The camera is aligned such that the angle with the parallel fences is 75°. What is the measure of the co-interior angle on the opposite side of the fences?

Answer: 105

Question 9: A researcher observes two parallel mountain ridges and notes the angle between a nearby trail and one ridge as 50°. If the trail crosses the ridges, what is the measure of the co-interior angle on the other side of the trail?

Answer: 130

Question 10: Explain why two co-interior angles formed by a transversal crossing parallel lines must always sum to 180°. Use a real-world example in your explanation.

Answer: Because the angles are supplementary on a straight line, and the parallel lines ensure the angles are equal to alternate interior angles, which are supplementary.

Question 11: An environmental scientist models the flow of water between two parallel channels. If the angle of flow with a boundary in one channel is 60°, what is the measure of the complementary co-interior angle in the adjacent channel?

Answer: 120

Question 12: Identify and correct the mistake in this reasoning: 'Since the angles are on a straight line, they must add up to 180°, so the co-interior angles on parallel lines are always equal.'

Answer: The mistake is that co-interior angles on parallel lines are supplementary, not necessarily equal.