Question

I just need r and s . I just need a brief explanation with the answer

Answer 1

In order to find r and s we need to solve the following system of equations:

$\begin{gathered} r=30x+40 \\ s=130x-160 \\ r=s \end{gathered}$$\begin{bmatrix}r=30x+40 \\ r=130x-160\end{bmatrix}$$130x-160=30x+40$$\begin{gathered} 130x-30x=40+160 \\ 100x=200 \\ x=\frac{200}{100} \\ x=2 \end{gathered}$

replace x = 2 in the initial equations

$\begin{gathered} r=30\cdot\: 2+40 \\ r=60+40 \\ r=100 \end{gathered}$$\begin{gathered} s=130\cdot\: 2-160 \\ s=260-160 \\ s=100 \end{gathered}$

take into account r and s are corresponding angles, that's why they are equal.