Question 1: In the diagram, two intersecting lines form four angles. Identify the pairs of vertically opposite angles and state their measures if one angle measures 65°.

Answer: Angles opposite to the 65° angle are 65°

Question 2: Construct two intersecting lines on the grid such that one pair of vertically opposite angles measures 110° and 70°. Label the angles distinctly.

Answer: The other pairs of vertically opposite angles are 110° and 70° respectively.

Question 3: A pair of intersecting lines form an angle of 50°. What are the measures of the vertically opposite angles? Explain your reasoning.

Answer: Vertical angles are equal; so the pair are both 50°.

Question 4: Plot two lines on the grid such that they intersect, forming angles of 45° and 135°. Identify the vertically opposite angles.

Answer: Vertical angles are 45° and 135° respectively.

Question 5: In a diagram, lines AB and CD intersect at point O. If angle AOB measures 120°, what is the measure of the vertically opposite angle COD?

Answer: 120°

Question 6: Identify the pairs of vertically opposite angles in this diagram and justify your choice. (Provide a brief explanation.)

Answer: Angles directly across each other at the intersection are vertically opposite because they are formed by the crossing lines and are equal.

Question 7: Given two intersecting lines where one angle measures 75°, find the measure of its vertically opposite angle.

Answer: 75°

Question 8: A diagram shows two lines crossing, forming four angles. If two adjacent angles are 80° and 100°, identify the vertically opposite angles and their measures.

Answer: Vertically opposite angles are equal to the given angles: 80° and 100° respectively.

Question 9: In a real-world scenario, two roads intersect forming four angles. If one of the angles is 60°, what are the measures of the vertically opposite angles? Explain how you determine this.

Answer: Vertical angles are equal; thus, the opposite angles are 60°.

Question 10: A challenging problem: Two intersecting lines form angles of 125° and 55°. Without measuring, determine the measures of the remaining two angles using properties of vertically opposite angles.

Answer: The remaining angles are 125° and 55°, as vertically opposite angles are equal.

Question 11: Identify the common mistake students make when assuming angles are supplementary rather than vertically opposite. Provide an example and correct it.

Answer: A student might incorrectly add angles to get 180°. Correct understanding: vertically opposite angles are equal, not necessarily supplementary unless they form a straight line.