Suggested Answer
To form a triangle the three angles must follow the inequality principle that says: The sum of any two sides must always be greater than the length of the third side. With this in mind let's check the angles.For the first item we have:[tex]\begin{gathered} 70+90>20\rightarrow160>20 \\ 70+20>90\rightarrow90>90 \\ 20+90>70\rightarrow110>90 \end{gathered}[/tex]Since the second inequality is invalid the angles don't form a triangle.For the second item we have:[tex]\begin{gathered} 55+45>75\rightarrow100>75 \\ 55+75>45\rightarrow130>45 \\ 45+75>55\rightarrow120>55 \end{gathered}[/tex]Since all the inequations are valid then the angles form a triangle. Since all the angles are smaller than 90 degrees, then this is an acute triangle.For the third item we have:[tex]\begin{gathered} 27+27>126\rightarrow54>126 \\ 27+126>27\rightarrow153>27 \end{gathered}[/tex]Since the second inequation is invalid, then the angles don't form a triangle.For the fourth item we have:[tex]\begin{gathered} 38+87>55\rightarrow125>55 \\ 38+55>87\rightarrow93>87 \\ 55+87>38\rightarrow142>38 \end{gathered}[/tex]Since all the inequalities are valid, then the angles form a triangle. All of its angles are smaller than 90 degrees, therefore this triangle is an acute triangle.