Question

Find the value of x in the image below

Answer 1

Check the picture below.

`\begin{cases} (x+16)+(7x+4)+y=180\\ ~\hfill y+(10x-10)=180 \end{cases}\qquad \begin{cases} (x+16)+(7x+4)=180-y\\ ~\hfill (10x-10)=180-y \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x+16)+(7x+4)~~ = ~~(10x-10)\implies 8x+20=10x-10 \\\\\\ 20=2x-10\implies 30=2x\implies \cfrac{30}{2}=x\implies \boxed{15=x} \\\\[-0.35em] ~\dotfill\\\\ 10x-10\implies 10(15)-10\implies\stackrel{\textit{the exterior angle}}{ 150-10\implies 140}`