Given:
[tex]\begin{gathered} HL\perp HJ \\ m\angle2=(a+15)º \\ m\angle3=(a+35)º \end{gathered}[/tex]
The angle formed between perpendicular lines is 90º, then, the sum of angles 2 and 3 is equal to 90º:
[tex]\begin{gathered} m\angle2+m\angle3=90 \\ \\ (a+15)º+(a+35)º=90 \end{gathered}[/tex]
Solve the equation above to a:
[tex]\begin{gathered} a+15+a+35=90 \\ 2a+50=90 \\ 2a=90-50 \\ 2a=40 \\ a=\frac{40}{2} \\ \\ a=20 \end{gathered}[/tex]
Then, the value of a is 20
