Question

given m||n, find the value of x. answer attempt 1 out of 3 x =

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((2x + 16)^{\circ}\) and \((6x+4)^{\circ}\) are alternate - exterior angles. Alternate - exterior angles are congruent when two parallel lines are cut by a transversal. So, \(2x + 16=6x + 4\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(16 = 6x+4 - 2x\), which simplifies to \(16 = 4x+4\).
Then subtract 4 from both sides: \(16−4=4x\), so \(12 = 4x\).
Divide both sides by 4: \(x=\frac{12}{4}=3\).

Answer:

\(x = 3\)