Question

given m || n, find the value of x and y. (3x - 20)° (y - 6)° (2x + 3)°

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(3x - 20=2x + 3\).
\[3x-2x=3 + 20\]
\[x = 23\]

Step2: Use linear - pair property

The angles \((3x - 20)^{\circ}\) and \((y - 6)^{\circ}\) form a linear - pair, so \((3x-20)+(y - 6)=180\). Substitute \(x = 23\) into the equation:
First, find the value of \(3x-20\) when \(x = 23\). \(3\times23-20=69 - 20=49\).
Then, \(49+(y - 6)=180\).
\[y-6=180 - 49\]
\[y-6=131\]
\[y=137\]

Answer:

\(x = 23\), \(y = 137\)