Question

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

Explanation:

Step1: Use property of parallel lines

Since \(m\parallel n\), the corresponding - angles are equal. So, \(8x + 1=9x - 16\).

Step2: Solve for \(x\)

Subtract \(8x\) from both sides: \(8x + 1-8x=9x - 16-8x\), which gives \(1=x - 16\). Then add 16 to both sides: \(x=1 + 16=17\).

Step3: Use another angle - relationship

The angles \((4y + 3)^{\circ}\) and \((9x - 16)^{\circ}\) are supplementary (linear - pair). Substitute \(x = 17\) into \(9x-16\), we get \(9\times17-16=153 - 16 = 137\).
Since \((4y + 3)+(9x - 16)=180\) (linear - pair of angles), and \(9x - 16 = 137\), then \(4y+3+137 = 180\), or \(4y+140 = 180\).

Step4: Solve for \(y\)

Subtract 140 from both sides: \(4y+140 - 140=180 - 140\), so \(4y = 40\). Divide both sides by 4: \(y=\frac{40}{4}=10\).

Answer:

\(x = 17\), \(y = 10\)