Question

given ( m parallel n ), find the value of ( x ) and ( y ).

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel n\), the angles \((9x - 14)^{\circ}\) and \((7x+18)^{\circ}\) are alternate interior angles. So \(9x-14=7x + 18\).

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Step2: Find the value of \(y\)

First, find the measure of \((7x + 18)^{\circ}\) when \(x = 16\). Substitute \(x=16\) into \(7x+18\), we get \(7\times16+18=112 + 18=130\).
Since \((7x + 18)^{\circ}\) and \(y^{\circ}\) are supplementary angles (they form a linear - pair), \(y=180-(7x + 18)\). Substitute \(x = 16\) into it, \(y=180-130 = 50\)

Answer:

\(x = 16\) and \(y=50\)