We know that:
Since line m is parallel to line n, (6x - 5) and (6x + 5) are a linear pair.
Linear pair means that the sum of two angles equaling 180°.
This means that:
[tex](6x - 5) + (6x + 5) = 180[/tex]
Step-by step calculations:
Opening the parenthesis:
[tex](6x - 5) + (6x + 5) = 180 \\\\6x - 5 + 6x + 5 = 180[/tex]
Combining like terms:
[tex]6x - 5 + 6x + 5 = 180 \\\\ (6x + 6x) + (-5 + 5) = 180[/tex]
Simplify the LHS:
[tex](6x + 6x) + (-5 + 5) = 180\\\\(12x) = 180[/tex]
Divide 12 both sides and simplify:
[tex]\frac{12x}{12} = \frac{180}{12} \\\\ x = 15[/tex]
Thus, the value of x is 15.
