Question

find the value of x for which a is parallel to b. the diagram is not to scale. (3x + 16)° (5x - 54)°

Explanation:

Step1: Set up equation for non - parallel condition

If lines \(a\) and \(b\) were parallel, the corresponding angles would be equal. Since we want them non - parallel, we assume the non - equality of the angles. Let's consider the fact that if the angles were equal (parallel case), we would have \(3x + 16=5x-54\). But for non - parallel, we solve this equation to find the 'break - point' value.
\[3x + 16=5x-54\]

Step2: Rearrange the equation

Subtract \(3x\) from both sides:
\[16 = 5x-3x-54\]
\[16=2x - 54\]

Step3: Solve for \(x\)

Add 54 to both sides:
\[16 + 54=2x\]
\[70 = 2x\]
Divide both sides by 2:
\[x = 35\]
So for \(x
eq35\), \(a\) is not parallel to \(b\).

Answer:

\(x
eq35\)