Question 1: In the figure, two parallel lines are cut by a transversal. If one co-interior angle measures 65°, find the other co-interior angle.

Answer: 115

Question 2: Construct a diagram showing two parallel lines cut by a transversal where two co-interior angles are 80° and x. Calculate x.

Answer: 100

Question 3: Explain why co-interior angles are supplementary when two lines are parallel.

Answer: Because they form a linear pair on the same side of the transversal, and supplementary angles sum to 180°, which is true only if lines are parallel.

Question 4: The co-interior angles on a transversal cut across two lines are 70° and x. Find x and explain your reasoning.

Answer: 110

Question 5: Draw a pair of parallel lines cut by a transversal where the co-interior angles are 120° and 60°. Verify the relationship between these angles.

Answer: They are supplementary, since 120° + 60° = 180°.

Question 6: A transversal cuts two parallel lines. If one co-interior angle is x and the other is 180° - x, what is the value of x? Show your reasoning.

Answer: 90

Question 7: A student claims that co-interior angles are always equal. Is this true? Justify your answer.

Answer: No, co-interior angles are equal only when the angles are alternating angles. When the lines are parallel, they are supplementary, not necessarily equal.

Question 8: Construct a diagram where two parallel lines are intersected by a transversal, creating a pair of co-interior angles that are both 75°. Confirm the supplementary relationship.

Answer: Since both angles are 75°, their sum is 150°, which is less than 180°, so they are not supplementary unless they are on different parts of the transversal.

Question 9: In a practical scenario, a carpenter measures angles where two beams are cut at 100° and x. If the beams are parallel and the angles are co-interior, find x.

Answer: 80

Question 10: Identify and correct the mistake: 'Co-interior angles are always equal when lines are parallel.'

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