Question

1. find x and y in the diagram below, where a transversal intersects two parallel line segments: 13x + 9 4x + 1 8y

Explanation:

Step1: Use the property of supplementary angles

When a transversal intersects two parallel lines, \(13x + 9\) and \(4x+1\) are supplementary. So, \((13x + 9)+(4x + 1)=180\).
Simplify the left - hand side: \(13x+4x+9 + 1=180\), which is \(17x+10 = 180\).
Subtract 10 from both sides: \(17x=180 - 10=170\).
Divide both sides by 17: \(x=\frac{170}{17}=10\).

Step2: Use the property of vertical angles and parallel lines

First, find \(4x + 1\) when \(x = 10\). Substitute \(x = 10\) into \(4x+1\), we get \(4\times10+1=41\).
Since \(4x + 1\) and \(8y\) are equal (vertical angles and parallel - line properties), then \(8y=41\).
Divide both sides by 8: \(y=\frac{41}{8}=5.125\).

Answer:

\(x = 10\), \(y=5.125\)