Question

given m||n, find the value of x. (4x - 8)° (7x - 20)° answer attempt 1 out of 2

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((4x - 8)^{\circ}\) and \((7x-20)^{\circ}\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So, \(4x-8=7x - 20\).

Step2: Solve the equation for \(x\)

First, subtract \(4x\) from both sides of the equation:
\(4x-8-4x=7x - 20-4x\)
\(-8 = 3x-20\).
Then, add 20 to both sides:
\(-8 + 20=3x-20 + 20\)
\(12 = 3x\).
Finally, divide both sides by 3:
\(\frac{12}{3}=\frac{3x}{3}\)
\(x = 4\).

Answer:

\(x = 4\)