In a right triangle, the acute angles are complementary angles, which means that their measures add up to 180º. Then:
[tex]m\angle L+m\angle K=180[/tex]
Replace the expressions for the measure of L and K in terms of x. Then, solve for x and substitute its value back into the expressions for L and K to find their values. Since angle J is a right angle, its measure is 90º.
[tex]\begin{gathered} m\angle L=2x+17 \\ m\angle K=3x+28 \\ \Rightarrow(2x+17)+(3x+28)=90 \end{gathered}[/tex]
Solve for x:
[tex]\begin{gathered} \Rightarrow5x+45=90 \\ \Rightarrow5x=90-45 \\ \Rightarrow5x=45 \\ \Rightarrow x=\frac{45}{5} \\ \Rightarrow x=9 \end{gathered}[/tex]
Replace x=9into the expressions for L and K:
[tex]\begin{gathered} m\angle K=3x+28 \\ =3(9)+28 \\ =27+28 \\ =55 \end{gathered}[/tex][tex]\begin{gathered} m\angle L=2x+17 \\ =2(9)+17 \\ =18+17 \\ =35 \end{gathered}[/tex]
Therefore, the measures of the angles are:
[tex]\begin{gathered} m\angle J=90 \\ m\angle K=55 \\ m\angle L=35 \end{gathered}[/tex]
