Question 1: In the diagram, two intersecting lines form vertically opposite angles. If one of the angles measures 65°, calculate the other vertically opposite angle.

Answer: 65

Question 2: Two lines intersect and form an angle of 110°. What is the measure of the vertically opposite angle?

Answer: 110

Question 3: Construct two intersecting lines on the grid that form a pair of vertically opposite angles measuring 45° and 135°. Show your working.

Answer: Construct lines with angles 45° and 135° at the intersection; vertically opposite angles are equal.

Question 4: In a diagram, two intersecting lines form one angle of 120°. Calculate the measure of the vertically opposite angle.

Answer: 120

Question 5: A pair of vertically opposite angles are 75° and an unknown angle. What is the measure of the unknown angle?

Answer: 75

Question 6: Two intersecting lines form an angle of 60°. Find the measure of the vertically opposite angle.

Answer: 60

Question 7: In a real-world scenario, two roads intersect. An angle measured at the intersection is 85°. What is the measure of the vertically opposite angle?

Answer: 85

Question 8: Two lines intersect, forming angles of 50° and 130°. Construct a diagram to represent this and identify all vertically opposite angles.

Answer: Construct lines intersecting with angles 50° and 130°, vertically opposite angles are equal to these measures respectively.

Question 9: A pair of vertically opposite angles are 95°. A third angle adjacent to one of these angles is 55°. Calculate the remaining angles around the point.

Answer: Vertically opposite angles are 95°, adjacent angles sum with 55° to 180°, so the remaining angles are 55°, 85°, and 85°.

Question 10: Challenge: Two lines intersect at an angle of 70°. Find the measure of the other vertically opposite angles, and explain why they are equal.

Answer: The vertically opposite angles are also 70°, because vertically opposite angles are always equal when two lines intersect.