Question 1: Calculate the value of angle x if it forms part of a C-pattern with a 120° co-interior angle.

Answer: 60

Question 2: In a pair of parallel lines cut by a transversal, if one co-interior angle is 95°, what is the other?

Answer: 95

Question 3: Construct a diagram showing two parallel lines cut by a transversal, with a C-pattern where one angle is 100°. Label all angles.

Answer: See full answer key

Question 1: A pair of parallel lines are cut by a transversal. If one co-interior angle is 65°, what is the measure of the corresponding alternate interior angle on the same side? Explain your reasoning.

Answer: 115° because alternate interior angles are equal and supplementary to co-interior angles in a C-pattern.

Question 2: Two parallel lines are intersected by a transversal, forming a C-pattern. If one angle in the pattern is 110°, draw and label the angles to find the unknowns. What are the measures of the other angles?

Answer: See full answer key

Question 1: A skyscraper has two vertical walls with a horizontal beam connecting them at the top. The beams form a C-pattern with the walls. If the interior angles at the top are 85° and 100°, how are the angles related? Draw the scenario and justify your answer.

Answer: They are co-interior angles; their measures sum to 180°, showing they are supplementary in the pattern.

Question 1: Construct a diagram of two parallel lines cut by a transversal where the angles in the C-pattern are not directly given but relate by algebraic expressions. Find the values of all angles if one is expressed as 2x + 10 and another as x + 40, with the total summing appropriately.

Answer: See full answer key

Question 2: Prove that if two co-interior angles in a C-pattern are both greater than 90°, then the lines are not parallel. Provide a detailed explanation.

Answer: If both angles are greater than 90°, their sum exceeds 180°, which contradicts the supplementary property of co-interior angles in parallel lines.

Question 1: A student calculates one co-interior angle as 70° and claims the other is 110° without drawing. Is this correct? Identify and explain any misconception.

Answer: No, because co-interior angles in a C-pattern are supplementary and should add up to 180°.

Question 2: A student draws two parallel lines and labels one angle as 85° in a C-pattern but then concludes the other angles are also 85°, claiming they are vertically opposite. Is this a correct application? Explain your reasoning.

Answer: No, because in a C-pattern, co-interior angles are equal only if the lines are parallel, but their positions matter—these angles are not necessarily vertically opposite.