Question

1. solve for y. a. y = 25 b. y = 5 c. y = 140 d. y = 40

Explanation:

Step1: Assume parallel - line relationships

If the lines are parallel, then the corresponding angles are equal. Let's assume the angles formed by the parallel lines and the transversals give us an equation based on angle - equality. If we assume that \(8x\) and \(6x + 10\) are corresponding angles (or alternate - interior/exterior angles depending on the parallel - line setup), then \(8x=6x + 10\).
\[8x-6x=6x + 10-6x\]
\[2x=10\]
\[x = 5\]

Step2: Use another angle - relationship to find \(y\)

Let's assume that \(6y-10\) and one of the other angles (say \(8x\)) are supplementary (a common angle - relationship in parallel - line setups). Since \(x = 5\), then \(8x=40\).
If \(6y-10\) and \(8x\) are supplementary, then \((6y-10)+8x=180\). Substitute \(x = 5\) (so \(8x = 40\)) into the equation:
\[6y-10+40=180\]
\[6y+30=180\]
\[6y=180 - 30\]
\[6y=150\]
\[y = 25\]

Answer:

A. \(y = 25\)