Question

which angles are supplementary to each other?
\\(\angle 7\\) and \\(\angle 3\\)
\\(\angle 5\\) and \\(\angle 1\\)
\\(\angle 12\\) and \\(\angle 3\\)
\\(\angle 1\\) and \\(\angle 4\\)

Explanation:

Define supplementary angles

Using the Supplementary Angles knowledge point
Two angles are supplementary if the sum of their measures is \(180^\circ\).

Identify linear pairs

Using the Linear Pair knowledge point
When two lines intersect, adjacent angles that lie on the same straight line form a linear pair and are supplementary.

Analyze the given options

Using the Supplementary Angles and Linear Pair knowledge points

• \(\angle 7\) and \(\angle 3\): These are located at different intersections and are not supplementary.
• \(\angle 5\) and \(\angle 1\): These are located at different intersections and are not supplementary.
• \(\angle 12\) and \(\angle 3\): These are located at different intersections and are not supplementary.
• \(\angle 1\) and \(\angle 4\): These two angles lie adjacent to each other along the same straight line at their intersection, forming a linear pair. Therefore, they must be supplementary.

Answer:

• \(\angle 7\) and \(\angle 3\)
• \(\angle 5\) and \(\angle 1\)
• \(\angle 12\) and \(\angle 3\)
• \(\angle 1\) and \(\angle 4\) (Correct answer)