Question

given ( l parallel m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify supplementary angles

The angle $(2x+20)^\circ$ and $54^\circ$ are same-side exterior angles, so they are supplementary (sum to $180^\circ$).
$$(2x+20) + 54 = 180$$

Step2: Simplify the equation

Combine constant terms on the left.
$$2x + 74 = 180$$

Step3: Isolate the variable term

Subtract 74 from both sides.
$$2x = 180 - 74$$
$$2x = 106$$

Step4: Solve for x

Divide both sides by 2.
$$x = \frac{106}{2}$$

Answer:

$x = 53$