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, \(3x - 20=2x + 3\).
\[3x-2x=3 + 20\]

Step2: Solve for \(x\)

Combining like - terms in the equation \(3x-2x=3 + 20\), we get \(x = 23\).

Step3: Find the value of the angle

Substitute \(x = 23\) into the expression for one of the angles. Let's use the angle \((3x - 20)^{\circ}\). Then \(3x-20=3\times23-20=69 - 20=49^{\circ}\).

Step4: Solve for \(y\)

Since the angle \((y - 6)^{\circ}\) is equal to the angle \((3x - 20)^{\circ}\) (corresponding angles), we have \(y-6 = 49\). Then \(y=49 + 6=55\).

Answer:

\(x = 23\), \(y = 55\)