Question

solve for x. x =
give answer
(10x - 2)° 102° (diagram: parallel lines cut by transversal, angles at intersections)

Explanation:

Step1: Identify the relationship

Since lines QR and ST are parallel (marked by the red ticks) and line OP is a transversal, the corresponding angles \((10x - 2)^\circ\) and \(102^\circ\) are equal. So we set up the equation:
\(10x - 2 = 102\)

Step2: Solve for x

Add 2 to both sides of the equation:
\(10x - 2 + 2 = 102 + 2\)
\(10x = 104\)

Divide both sides by 10:
\(x = \frac{104}{10}\)
Simplify the fraction:
\(x = 10.4\) (or as a fraction, \(x=\frac{52}{5}\))

Answer:

\(10.4\) (or \(\frac{52}{5}\))