Answer:
[tex]102\textdegree[/tex]
Step-by-step explanation:
If we let the measure of the smallest angle be [tex]x[/tex], then we know that the measure of the angle that is three times as large as it is [tex]3*x=3x[/tex] and the measure of the angle that is [tex]10\textdegree[/tex] larger than it is [tex]x+10[/tex].
Because the sum of the measures of the interior angles in a triangle is [tex]180\textdegree[/tex], we can write the following equation to solve for [tex]x[/tex]:
[tex]x+3x+x+10=180[/tex]
Solving for [tex]x[/tex], we get:
[tex]x+3x+x+10=180[/tex]
[tex]5x+10=180[/tex] (Combine like terms)
[tex]5x=170[/tex] (Subtract [tex]10[/tex] from both sides of the equation to isolate [tex]x[/tex], Simplify)
[tex]x=34\textdegree[/tex]
Therefore, the measures of the other angles are [tex]3x = 3 * 34=102\textdegree[/tex] and [tex]34+10=44\textdegree[/tex]. Since [tex]102>44>34[/tex], the measure of the largest angle will be [tex]\bf102\textdegree[/tex]. Hope this helps!
