Question

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

Explanation:

Step1: Identify supplementary angles

Since \(m \parallel n\), the two given angles are same-side exterior angles, so they are supplementary (sum to \(180^\circ\)).
$$(6x+14) + (5x+12) = 180$$

Step2: Combine like terms

Add the variable terms and constant terms.
$$11x + 26 = 180$$

Step3: Isolate the variable term

Subtract 26 from both sides of the equation.
$$11x = 180 - 26$$
$$11x = 154$$

Step4: Solve for x

Divide both sides by 11.
$$x = \frac{154}{11}$$

Answer:

\(x = 14\)