Question 1: When two lines intersect, what is the relationship between the pairs of vertically opposite angles? Briefly explain.

Answer: Vertically opposite angles are equal.

Question 2: Identify the pair of vertically opposite angles in the following scenario: Two intersecting lines form four angles. Angle A is 60°, and adjacent to it is angle B. What is the measure of the angle vertically opposite to angle A?

Answer: 60°

Question 3: Construct two intersecting lines on the grid so that one pair of vertically opposite angles measures 45° and 135°. Show your construction.

Answer: Construct lines intersecting with angles of 45° and 135° at the intersection, ensuring angles are opposite.

Question 4: In a diagram, two lines intersect, and one of the angles measures 110°. What are the measures of the vertically opposite angles?

Answer: 110° and 110°

Question 5: Explain why vertically opposite angles are always equal when two lines intersect. Use a diagram if necessary.

Answer: When two lines intersect, the angles formed are supplementary in pairs, and the pairs of angles opposite each other are equal because they are congruent angles formed by the intersecting lines.

Question 6: A transversal cuts two parallel lines, forming several angles. Identify which pairs of angles are vertically opposite and state their measures if one of the angles is 70°.

Answer: The vertically opposite angles are 70° and 70°.

Question 7: A diagram shows two intersecting lines forming four angles. Two adjacent angles are 65° and 115°. What are the measures of the vertically opposite angles?

Answer: 65° and 65°

Question 8: A student incorrectly states that vertically opposite angles are always supplementary. Is this true or false? Explain your answer.

Answer: False. Vertically opposite angles are always equal, not necessarily supplementary unless they are 90° angles.

Question 9: Plot on the grid two straight lines intersecting at a point. Mark one of the angles as 120°. Use the grid to indicate the measures of the vertically opposite angles.

Answer: The vertically opposite angles are 120° and 120°.

Question 10: Identify a common mistake students make when first learning about vertically opposite angles and how to correct it.

Answer: A common mistake is thinking angles adjacent to each other are equal; correction: vertically opposite angles are equal, but adjacent angles are supplementary.

Question 11: Challenge: Two intersecting lines form angles of 85° and 95°. What are the measures of the other two angles? Show your reasoning.

Answer: The other two angles are 85° and 95° as vertically opposite angles are equal, and the adjacent angles sum to 180°.