Question

question given m || n, find the value of x and y. answer attempt 1 out of 3 x = y = due december 14 at 8:00 pm grade 54% transversal problems with equations (level 2) angles formed by parallel lines

Explanation:

Step1: Use property of corresponding angles

Since \(m\parallel n\), the angles \((8x + 1)^{\circ}\) and \((9x-4)^{\circ}\) are corresponding angles and are equal. So we set up the equation \(8x + 1=9x - 4\).

$$8x+1 = 9x - 4$$

Step2: Solve the equation for \(x\)

Subtract \(8x\) from both sides: \(1=x - 4\). Then add 4 to both sides to get \(x=5\).

$$1+4=x$$

$$x = 5$$

Step3: Find the value of \(y\)

The angle \((8x + 1)^{\circ}\) and \(y^{\circ}\) are supplementary (linear - pair), so \(y+(8x + 1)=180\). Substitute \(x = 5\) into \(8x+1\): \(8\times5+1=40 + 1=41\). Then \(y=180-(8x + 1)=180 - 41 = 139\).

$$y=180-(8\times5 + 1)$$

$$y = 139$$

Answer:

\(x = 5\)
\(y=139\)