Question 1: If two intersecting lines form a pair of vertically opposite angles measuring 65°, find the measures of the other pair of vertically opposite angles.

Answer: 65

Question 2: Calculate the value of the unknown angle if it is vertically opposite to an angle measuring 40°.

Answer: 40

Question 3: Construct two intersecting lines such that one of the angles formed measures 120°. Use the grid to accurately draw the lines and label the angles.

Answer: Constructed lines with angles 120° and 60°, vertically opposite angles both 120°.

Question 4: In a diagram, two lines intersect and form angles of 75° and 105°. What are the measures of the other two vertically opposite angles?

Answer: 75, 105

Question 5: A pair of vertically opposite angles are known to measure 50° and 130°. If the lines are extended, what is the measure of the angle directly opposite the 50° angle?

Answer: 50

Question 6: A transversal cuts two parallel lines, forming one angle of 70°. Find the measure of the corresponding vertically opposite angle.

Answer: 70

Question 7: Calculate the measure of an angle that is vertically opposite to an angle of 85°.

Answer: 85

Question 8: Two lines intersect to form four angles. If one angle is 60°, what are the measures of the other three angles?

Answer: 60°, 120°, 120°

Question 9: In a diagram, two intersecting lines form angles of 110° and x°. The angles are vertically opposite. Find the value of x.

Answer: 110

Question 10: Identify and correct the mistake in the following reasoning: "Since two angles are vertically opposite and one measures 95°, the other must also be 95°."

Answer: This is correct; no mistake.

Question 11: A pair of vertically opposite angles are each 125°. If a third angle adjacent to one of these is 55°, what is the measure of the other adjacent angle?

Answer: 125