Question 1: Calculate the measure of angle A if it is part of a C-pattern with a 120° angle on the same transversal crossing parallel lines.

Answer: 60

Question 2: If the two co-interior angles are supplementary and one angle measures 75°, what is the value of the other?

Answer: 105

Question 3: On a diagram, two parallel lines are crossed by a transversal. If one angle in the C-pattern is 85°, find the corresponding co-interior angle.

Answer: 95

Question 4: Construct a diagram on the grid showing two parallel lines and a transversal with a C-pattern where one co-interior angle is 110°. Label all angles.

Answer: See diagram for correct angles

Question 1: Two parallel lines are cut by a transversal, forming a C-pattern with one angle measuring 130°. Find the measures of the other three angles in the pattern. Explain your reasoning.

Answer: Angles are 50°, 50°, and 130°; co-interior angles are supplementary, so each pair sums to 180°.

Question 2: In a real-world scenario, a road intersects a railway track with two parallel tracks. The transversal line represents a security barrier. If one co-interior angle is 70°, what is the angle on the opposite side of the barrier? Justify your answer.

Answer: 70°, because co-interior angles are equal when lines are parallel and the barrier acts as the transversal.

Question 3: A student claims that all angles in a C-pattern are equal. Using a diagram, evaluate and explain if this is true or false.

Answer: False; co-interior angles are supplementary, not necessarily equal, unless they are 90°.

Question 1: A city planner designs a crossing with two parallel roads and a transversal for pedestrian pathways. If one angle in the C-pattern is 45°, determine all other angles formed around the crossing. Explain how this helps ensure safety.

Answer: Angles are 45°, 135°, 45°, and 135°; understanding the C-pattern helps in designing crossings that are easy to navigate and safe.

Question 1: Prove that if a transversal crosses two parallel lines, then the sum of the measures of the two co-interior angles in the C-pattern is always 180°. Include a formal proof.

Answer: Since co-interior angles are supplementary when lines are parallel, their sum is 180°. Proof involves alternate interior angles and properties of parallel lines.

Question 2: Design a complex diagram with multiple transversal lines crossing a set of parallel lines to create several C-patterns. Identify and label all pairs of co-interior angles and verify their supplementary nature.

Answer: Diagram should show multiple transversals with angles labeled; all co-interior pairs sum to 180°.

Question 3: A new type of angle pattern emerges when lines are not perfectly parallel. Describe how the properties of the C-pattern change and what methods can be used to verify angles are supplementary.

Answer: Angles may no longer be supplementary if lines are not parallel. Use of alternate interior angles, transversal properties, and measurement can verify angle relationships.

Question 1: A student claims that in a C-pattern, the angles are always equal. Provide an example where this is incorrect and explain why.

Answer: Incorrect; in a C-pattern, co-interior angles are supplementary, not necessarily equal unless both are right angles.

Question 2: Identify and correct the mistake in this reasoning: 'Since the angles are equal in the C-pattern, they must both measure 90°.'

Answer: Incorrect; angles are equal only if they are right angles, which is not necessarily true in all C-patterns.