Question 1: Calculate the value of angle x if it is vertically opposite to a 60° angle.

Answer: 60

Question 2: In the diagram, two intersecting lines form an angle of 125°. Find the measure of the vertically opposite angle.

Answer: 125

Question 3: A pair of vertically opposite angles are each x degrees. If one angle is 45°, find x.

Answer: 45

Question 4: Construct two intersecting lines to form an angle of 70°. Calculate the measure of the vertically opposite angle.

Answer: 70

Question 1: Lines AB and CD intersect at point O, forming an angle of 110°. Find the measure of the vertically opposite angle, and explain why these angles are equal.

Answer: 110; Vertically opposite angles are equal because when two lines intersect, the angles opposite each other are equal.

Question 2: Given two intersecting lines with one angle measuring 85°, find all four angles around the intersection point. Show your calculations.

Answer: 85, 85, 95, 95

Question 1: A carpenter cuts two pieces of wood that intersect, forming angles. If one of the angles is 70°, what is the measure of the vertically opposite angle? How might this knowledge be useful in ensuring a proper joint?

Answer: 70; Vertically opposite angles are equal, so the other angle is 70°. This helps in making precise cuts for accurate joints.

Question 1: Lines XY and ZW intersect at point P, creating an angle of 130°. A third line intersects XY at point Q, forming an adjacent angle of 55°. Calculate the measure of the vertically opposite angle at P, considering the intersecting lines, and justify your answer.

Answer: 130

Question 2: In a complex diagram, multiple intersecting lines form various angles. If two intersecting lines produce an angle of 120°, determine all possible angles around the intersection point, assuming symmetrical properties. Explain your reasoning.

Answer: 120, 120, 60, 60

Question 1: A student states that in intersecting lines, the angles of 65° and 115° are vertically opposite. Is this correct? If not, identify the mistake and provide the correct reasoning.

Answer: No; Vertically opposite angles are equal, so if one angle is 65°, the opposite angle must also be 65°, not 115°.

Question 2: Correct the following statement: 'Angles formed by intersecting lines are always supplementary.'

Answer: Angles formed by intersecting lines are vertically opposite and equal, not necessarily supplementary.