Question

If m/_KNM = (8x - 5)° and m/_MNJ =(4x - 19)° . Find the m/_LNJ.Value of x: m/_LNJ = degrees

Answer 1

`\begin{gathered} \text{If KNM=8x-5} \\ \text{KNM}=\text{LNJ (Opposite angles are equal)} \\ \text{Therefore LNJ=8x-5} \\ \text{Also;} \\ \text{MNJ}+\text{LNJ}=180\text{ (Angles on a straight line add up to 180)} \\ \text{Therefore;} \\ 4x-19+8x-5=180 \\ 12x-24=180 \\ 12x=180+24 \\ 12x=204 \\ \text{Divide both sides by 12} \\ x=17 \\ \text{If LNJ is 8x-5, then} \\ 8(17)-5=\text{LNJ} \\ 136-5=\text{LNJ} \\ \text{LNJ}=131 \end{gathered}`