Question

given m || n, find the value of x and y.
answer attempt 2 out of 2
x =
y =

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), the angles \((8x + 1)^{\circ}\) and \((9x-16)^{\circ}\) are congruent (alternate - interior angles).
So, \(8x+1=9x - 16\).
Subtract \(8x\) from both sides: \(1=x - 16\).
Add \(16\) to both sides: \(x=17\).

Step2: Find the value of \(y\)

Substitute \(x = 17\) into \((8x + 1)^{\circ}\): \(8\times17+1=136 + 1=137^{\circ}\).
Since \(m\parallel n\), \((8x + 1)^{\circ}\) and \((4y+3)^{\circ}\) are supplementary (same - side interior angles).
So, \((4y + 3)+(8x + 1)=180\).
Substitute \(x = 17\): \(4y+3+137=180\).
Simplify: \(4y+140=180\).
Subtract \(140\) from both sides: \(4y=40\).
Divide both sides by \(4\): \(y = 10\).

Answer:

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