Question

Refer to the figure. If m2= (a+15)° and m3 = (a+35)

Answer 1

Given:

`\begin{gathered} HL\perp HJ \\ m\angle2=(a+15)º \\ m\angle3=(a+35)º \end{gathered}`

The angle formed between perpendicular lines is 90º, then, the sum of angles 2 and 3 is equal to 90º:

`\begin{gathered} m\angle2+m\angle3=90 \\ \\ (a+15)º+(a+35)º=90 \end{gathered}`

Solve the equation above to a:

`\begin{gathered} a+15+a+35=90 \\ 2a+50=90 \\ 2a=90-50 \\ 2a=40 \\ a=(40)/(2) \\ \\ a=20 \end{gathered}`

Then, the value of a is 20