Question

given $m\parallel n$, find the value of x.

Explanation:

Step1: Identify supplementary angles

The angles $(2x+2)^\circ$ and $(x+16)^\circ$ are supplementary (they form a linear pair on line $n$), so their sum equals $180^\circ$.
$$(2x+2) + (x+16) = 180$$

Step2: Simplify the equation

Combine like terms on the left side.
$$3x + 18 = 180$$

Step3: Isolate the term with $x$

Subtract 18 from both sides of the equation.
$$3x = 180 - 18$$
$$3x = 162$$

Step4: Solve for $x$

Divide both sides by 3.
$$x = \frac{162}{3}$$

Answer:

$x = 54$