To determine which set of three angles could represent the interior angles of a triangle, we need to observe one fundamental property: the sum of the interior angles in a triangle always equals [tex]\(180^\circ\)[/tex].
Let's examine each set of angles:
1. Set 1: [tex]\(26^\circ, 51^\circ, 103^\circ\)[/tex]
- Sum of angles: [tex]\(26^\circ + 51^\circ + 103^\circ = 180^\circ\)[/tex]
- Since the sum is [tex]\(180^\circ\)[/tex], this set could represent the interior angles of a triangle.
2. Set 2: [tex]\(29^\circ, 54^\circ, 107^\circ\)[/tex]
- Sum of angles: [tex]\(29^\circ + 54^\circ + 107^\circ = 190^\circ\)[/tex]
- Since the sum is not [tex]\(180^\circ\)[/tex], this set cannot represent the interior angles of a triangle.
3. Set 3: [tex]\(35^\circ, 35^\circ, 20^\circ\)[/tex]
- Sum of angles: [tex]\(35^\circ + 35^\circ + 20^\circ = 90^\circ\)[/tex]
- Since the sum is not [tex]\(180^\circ\)[/tex], this set cannot represent the interior angles of a triangle.
4. Set 4: [tex]\(10^\circ, 90^\circ, 90^\circ\)[/tex]
- Sum of angles: [tex]\(10^\circ + 90^\circ + 90^\circ = 190^\circ\)[/tex]
- Since the sum is not [tex]\(180^\circ\)[/tex], this set cannot represent the interior angles of a triangle.
Based on the sums calculated:
- Set 1 with angles [tex]\(26^\circ, 51^\circ, 103^\circ\)[/tex] is the only set that sums up to [tex]\(180^\circ\)[/tex].
Therefore, Set 1 could represent the interior angles of a triangle.
