Question

which angles are vertical to each other?

\\(\angle 2\\) and \\(\angle 4\\)
\\(\angle 10\\) and \\(\angle 11\\)
\\(\angle 1\\) and \\(\angle 2\\)
\\(\angle 16\\) and \\(\angle 4\\)

Explanation:

Define vertical angles

Using the Vertical Angles knowledge point
Vertical angles are pairs of non-adjacent angles formed by two intersecting straight lines. They lie opposite each other across the intersection point and share only a vertex.

Analyze the given options

Using the Vertical Angles knowledge point

• \(\angle 2\) and \(\angle 4\): These angles are formed by the intersection of two straight lines. They lie directly opposite each other at the intersection point, sharing only the vertex. Thus, they are vertical angles.
• \(\angle 10\) and \(\angle 11\): These angles lie adjacent to each other along a straight line, sharing a common side. They form a linear pair, not vertical angles.
• \(\angle 1\) and \(\angle 2\): These angles lie adjacent to each other along a straight line, sharing a common side. They form a linear pair, not vertical angles.
• \(\angle 16\) and \(\angle 4\): These angles are located at completely different intersection vertices and do not share a vertex. Thus, they cannot be vertical angles.

Identify the correct pair

Using the Vertical Angles knowledge point
The only pair of angles that are opposite each other at an intersection of two lines is \(\angle 2\) and \(\angle 4\).

Answer:

• \(\angle 2\) and \(\angle 4\) (Correct answer)
• \(\angle 10\) and \(\angle 11\)
• \(\angle 1\) and \(\angle 2\)
• \(\angle 16\) and \(\angle 4\)