Question

1. find the value of x.

3x = 102
/3 /3
x = 34
explain the mistake:
find the correct answer:

Explanation:

Step1: Analyze the relationship between angles

Since the two vertical lines are parallel, \(3x\) and \(102^{\circ}\) are supplementary angles. So \(3x + 102=180\).

Step2: Solve the equation for \(x\)

Subtract \(102\) from both sides of the equation \(3x + 102 = 180\):
\(3x=180 - 102\)
\(3x = 78\)
Divide both sides by \(3\):
\(x=\frac{78}{3}=26\)

Answer:

The mistake was that the original solution assumed \(3x = 102\) (they are not equal angles, but supplementary). The correct answer is \(x = 26\).