Question

Find the value of X thy would prove j || k. state the converse that justifies your answer.

Answer 1

Given two parallel lines and a transversal

The given angles: (2x-8) and (9x-10) are supplementary angles

So, the sum of the angles = 180

So,

`(2x-8)+(9x-10)=180`

Solve the equation to find x :

`\begin{gathered} 2x-8+9x-10=180 \\ 11x-18=180 \\ 11x=180+18 \\ 11x=198 \\ \\ x=(198)/(11)=18 \end{gathered}`

So, the answer will be x = 18

The converse of the solution:

when x = 18

So, the measure of the angles will be:

2x - 8 = 2 * 18 - 8 = 36 - 8 = 28

9x - 10 = 9 * 18 - 10 = 162 - 10 = 152

The sum of the angles are = 28 + 152 = 180

So, the sum of the angles = 180

So, the angles are supplementary angles

So, the lines J and K are parallel lines

so, J || K