Question

Given m| n, find the value of x. (7x-10)° m (6x-5)°

Answer 1

From the figure we note that the angles a and (6x-5) are vertically opposite, then they are equal. Furthermore tha angles a and b are also equal since they are alternate interior angles. From this we conclude that

`a=b=6x-5`

Once we know that, we see that the angles (7x-10) and b are supplementary then their sum should be 180. From those arguments we have the equation

`(7x-10)+(6x-5)=180`

Solving for x, we have

`\begin{gathered} (7x-10)+(6x-5)=180 \\ 7x-10+6x-5=180 \\ 13x-15=180 \\ 13x=180+15 \\ 13x=195 \\ x=(195)/(13) \\ x=15 \end{gathered}`

Then x=15 degrees.