Question 1: Calculate the missing angle in the diagram where the two co-interior angles are 65° and x°.

Answer: 115

Question 2: If one co-interior angle is 120°, what is the other co-interior angle?

Answer: 60

Question 3: Construct a pair of co-interior angles that sum to 180°, with one angle measuring 85°.

Answer: 95

Question 4: Identify the error in the following statement: 'Since the angles are on the same side of the transversal and between the parallel lines, they must sum to 180°.'

Answer: Incorrect because co-interior angles are on the same side but do not necessarily sum to 180° unless the lines are parallel.

Question 1: In a diagram, two parallel lines are cut by a transversal. One of the co-interior angles measures 130°. What is the measure of the other co-interior angle? Explain why.

Answer: 50; because co-interior angles on parallel lines sum to 180°

Question 2: Two angles are marked as 75° and 105° on a diagram with parallel lines cut by a transversal. Are these angles co-interior? Justify your answer.

Answer: Yes; they are co-interior angles because they are on the same side of the transversal between the lines and sum to 180°.

Question 3: Given the diagram shows a transversal crossing two parallel lines, with one co-interior angle labeled 110°, find the other co-interior angle and explain your reasoning.

Answer: 70; because co-interior angles sum to 180°

Question 1: A city road layout uses parallel roads crossed by a transversal at an intersection. If the angle between the transversal and one road is 65°, what is the measure of the co-interior angle on the opposite side? How could this knowledge help in designing the intersection?

Answer: 115; it helps in understanding the angles for safety and signage placement

Question 1: Construct a diagram with two parallel lines cut by a transversal, where one co-interior angle is 125°. Use the grid to accurately draw and label the angles, then verify the other angle.

Answer: 55

Question 2: Explain why co-interior angles are supplementary only when lines are parallel. Use a diagram to support your reasoning.

Answer: Because in parallel lines, co-interior angles are on the same side of the transversal and together form a straight line, summing to 180°; in non-parallel lines, this property does not necessarily hold.

Question 1: A student claims that co-interior angles always measure less than 180°. Is this true? Correct the misconception and provide an example.

Answer: No; co-interior angles can be equal to 180°, such as when they are supplementary in the case of parallel lines.

Question 2: Identify and correct the mistake in this statement: 'If two angles are co-interior and both measure 90°, then the lines are parallel.'

Answer: Incorrect; two angles both 90° do not necessarily imply the lines are parallel; they could be perpendicular or intersecting at a different angle.