Question

m∠1=(6x - 12)°
m∠2=(2x + 24)°
(the diagram is not drawn to scale.)
what equation would you use to prove m||n and what is the value of x?
a 6x - 12+2x + 24 = 90, x = 12
b 6x - 12+2x + 24 = 180, x = 21
c 6x - 12+2x + 24 = 180, x = 24
d 6x - 12 = 2x + 24, x = 9

Explanation:

Step1: Use the property of parallel lines

When \(m\parallel n\), \(\angle1\) and \(\angle2\) are corresponding angles. For lines \(m\) and \(n\) to be parallel, \(\angle1=\angle2\) (corresponding angles postulate). So the equation is \(6x - 12=2x + 24\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
\(6x-2x - 12=2x-2x + 24\)
\(4x-12 = 24\)
Add \(12\) to both sides:
\(4x-12 + 12=24+ 12\)
\(4x=36\)
Divide both sides by \(4\):
\(x=\frac{36}{4}=9\)

Answer:

D. \(6x - 12=2x + 24,x = 9\)