Question 1: In the diagram, two intersecting lines form angles A and B. If angle A measures 65°, what is the measure of the vertically opposite angle B?

Answer: 65

Question 2: Identify whether the following statement is true or false: 'Vertically opposite angles are always equal.'

Answer: true

Question 3: In a diagram, two lines intersect, creating angles X and Y. Angle X is 120°. Without measuring, determine the measure of the vertically opposite angle Y.

Answer: 120

Question 4: A student claims that vertically opposite angles can sometimes be different. Using an example or explanation, correct this misconception.

Answer: Vertically opposite angles are always equal because they are formed by two intersecting lines, which creates pairs of equal angles.

Question 5: Construct a pair of intersecting lines on the grid so that one pair of vertically opposite angles measures 45° and the other pair measures 135°. Label the angles accordingly.

Answer: Angles of 45° and 135° are vertically opposite pairs; they are equal in their respective pairs.

Question 6: Plot two intersecting lines on the grid such that one pair of vertically opposite angles are 70° and the other pair are 110°. Verify your construction.

Answer: Angles of 70° and 110° are vertically opposite in the diagram, ensuring the angles are correctly constructed.

Question 7: A diagram shows two lines intersecting, with angles labeled as 85° and 95°. Are these angles vertically opposite? Explain your reasoning.

Answer: No, because vertically opposite angles are equal. 85° and 95° are not equal, so they are not vertically opposite.

Question 8: Identify the common mistake in students who think that vertically opposite angles can sometimes be supplementary. How can this misconception be corrected?

Answer: The mistake is assuming angles are always supplementary when they are vertical. Correction involves emphasizing that vertically opposite angles are always equal, not necessarily supplementary.

Question 9: Given two intersecting lines forming four angles, two of which are marked as 50° and 130°. Are these angles vertically opposite? Justify your answer.

Answer: Yes, because vertically opposite angles are equal, and 50° and 130° are not equal, so they are not vertically opposite.

Question 10: Common Error: A student marks two angles as vertically opposite but states they are 60° and 80°. Identify and correct the mistake.

Answer: The mistake is assuming the angles are vertically opposite without checking their measures. Correctly, they must be equal for vertical angles, so if one is 60°, the opposite must also be 60°.

Question 11: Challenge Question: Construct and label a pair of intersecting lines on the grid where the vertically opposite angles are 110° and 70°, showing the angles clearly.

Answer: Angles of 110° and 70° are vertically opposite pairs; the construction must reflect their equality in pairs.