Question

which angles are supplementary to each other? select all that apply.

Explanation:

To determine supplementary angles, we use the definition: two angles are supplementary if their sum is \(180^\circ\) (they form a linear pair or are on a straight line).

Step 1: Analyze \(\angle 10\) and \(\angle 8\)

• If \(\angle 10\) and \(\angle 8\) are related by parallel lines (or linear pair logic), we check if they sum to \(180^\circ\). From the diagram, if lines are arranged such that these angles are on a straight - line - related path, they can be supplementary. But wait, actually, let's re - evaluate. Wait, no—wait, the correct way: \(\angle 6\) and \(\angle 7\): they form a linear pair (adjacent angles on a straight line), so \(\angle 6+\angle 7 = 180^\circ\), so they are supplementary. \(\angle 3\) and \(\angle 4\): they form a linear pair, so \(\angle 3+\angle 4=180^\circ\), supplementary. \(\angle 10\) and \(\angle 11\): they form a linear pair, so \(\angle 10+\angle 11 = 180^\circ\), supplementary. But \(\angle 10\) and \(\angle 8\): are they supplementary? Wait, maybe a mistake in the initial check. Let's correct:

Linear pair angles (adjacent angles that form a straight line) are supplementary.

• \(\angle 6\) and \(\angle 7\): Adjacent, form a straight line. So \(\angle 6+\angle 7 = 180^\circ\) (supplementary).
• \(\angle 3\) and \(\angle 4\): Adjacent, form a straight line. So \(\angle 3+\angle 4 = 180^\circ\) (supplementary).
• \(\angle 10\) and \(\angle 11\): Adjacent, form a straight line. So \(\angle 10+\angle 11=180^\circ\) (supplementary).
• \(\angle 10\) and \(\angle 8\): Do they form a linear pair? No. Wait, maybe the diagram has some parallel lines or transversals, but the key is linear pairs. So the correct supplementary pairs from the options (after correction) are \(\angle 6\) and \(\angle 7\), \(\angle 3\) and \(\angle 4\), \(\angle 10\) and \(\angle 11\). The \(\angle 10\) and \(\angle 8\) is incorrect.

Wait, let's start over. The definition of supplementary angles: sum to \(180^\circ\). Linear pair angles (adjacent, share a common side and vertex, and their non - common sides form a straight line) are supplementary.

1. For \(\angle 6\) and \(\angle 7\):

• They are adjacent, share a common vertex and side, and their non - common sides form a straight line. So \(\angle 6+\angle 7 = 180^\circ\) (supplementary).

1. For \(\angle 3\) and \(\angle 4\):

• They are adjacent, share a common vertex and side, and their non - common sides form a straight line. So \(\angle 3+\angle 4=180^\circ\) (supplementary).

1. For \(\angle 10\) and \(\angle 11\):

• They are adjacent, share a common vertex and side, and their non - common sides form a straight line. So \(\angle 10+\angle 11 = 180^\circ\) (supplementary).

1. For \(\angle 10\) and \(\angle 8\):

• They do not form a linear pair, and without more information (like parallel lines and transversals), we can't assume they are supplementary. So the initial check of \(\angle 10\) and \(\angle 8\) was wrong.

Answer:

The supplementary angle pairs are: \(\boldsymbol{\angle 6}\) and \(\boldsymbol{\angle 7}\), \(\boldsymbol{\angle 3}\) and \(\boldsymbol{\angle 4}\), \(\boldsymbol{\angle 10}\) and \(\boldsymbol{\angle 11}\)

(If we consider the options, the correct ones among the given are \(\angle 6\) and \(\angle 7\), \(\angle 3\) and \(\angle 4\), \(\angle 10\) and \(\angle 11\); \(\angle 10\) and \(\angle 8\) is incorrect)