Question

given m || n, find the value of x and y.

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(6x + 19=7x + 15\).

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides: \(19=x + 15\). Then subtract 15 from both sides: \(x=19 - 15=4\).

Step3: Find the value of \(y\)

First, find the measure of the angle \((6x + 19)^{\circ}\) by substituting \(x = 4\). So, \(6x+19=6\times4 + 19=24 + 19 = 43^{\circ}\).
Since \(y\) and \((6x + 19)\) are supplementary (a linear - pair), \(y=180-(6x + 19)\). Substituting \(x = 4\), we get \(y=180 - 43=137^{\circ}\).

Answer:

\(x = 4\), \(y = 137\)