To determine which set of three angles can represent the interior angles of a triangle, we need to know that the sum of the interior angles of any triangle must be [tex]\(180^\circ\)[/tex]. We will calculate the sum for each set of angles provided and check which one sums to [tex]\(180^\circ\)[/tex].
First set of angles: [tex]\(26^\circ\)[/tex], [tex]\(51^\circ\)[/tex], [tex]\(103^\circ\)[/tex]
[tex]\[
26^\circ + 51^\circ + 103^\circ = 180^\circ
\][/tex]
This set sums to [tex]\(180^\circ\)[/tex], so it could represent the interior angles of a triangle.
Second set of angles: [tex]\(29^\circ\)[/tex], [tex]\(54^\circ\)[/tex], [tex]\(107^\circ\)[/tex]
[tex]\[
29^\circ + 54^\circ + 107^\circ = 190^\circ
\][/tex]
This set sums to [tex]\(190^\circ\)[/tex], which is more than [tex]\(180^\circ\)[/tex], so it does not represent the interior angles of a triangle.
Third set of angles: [tex]\(35^\circ\)[/tex], [tex]\(35^\circ\)[/tex], [tex]\(20^\circ\)[/tex]
[tex]\[
35^\circ + 35^\circ + 20^\circ = 90^\circ
\][/tex]
This set sums to [tex]\(90^\circ\)[/tex], which is less than [tex]\(180^\circ\)[/tex], so it does not represent the interior angles of a triangle.
Fourth set of angles: [tex]\(10^\circ\)[/tex], [tex]\(90^\circ\)[/tex], [tex]\(90^\circ\)[/tex]
[tex]\[
10^\circ + 90^\circ + 90^\circ = 190^\circ
\][/tex]
This set sums to [tex]\(190^\circ\)[/tex], which is more than [tex]\(180^\circ\)[/tex], so it does not represent the interior angles of a triangle.
Since only the first set of angles sums to [tex]\(180^\circ\)[/tex], the set of angles that could represent the interior angles of a triangle is:
[tex]\[
26^\circ, 51^\circ, 103^\circ
\][/tex]
