Question

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

Explanation:

Step1: Use the property of parallel lines

When \( l\parallel m\parallel n\), the consecutive - interior angles formed by a transversal satisfy the relationship: \((7x + 11)+(3x + 19)=180\) (because the sum of consecutive - interior angles between two parallel lines is \(180^{\circ}\)).

Step2: Simplify the equation

Combine like terms:

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Subtract \(30\) from both sides of the equation: \(10x=180 - 30\), so \(10x=150\).
Divide both sides by \(10\): \(x=\frac{150}{10}\).

Answer:

\(x = 15\)