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.
