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 angle \((9x - 10)^{\circ}\) and the angle \((4x-5)^{\circ}\) are alternate - interior angles. So \(9x-10=4x - 5\).

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Step2: Use the property of corresponding angles

The angle \((9x - 10)^{\circ}\) and the angle \((y - 20)^{\circ}\) are corresponding angles. Substitute \(x = 15\) into \(9x-10\), we get \(9\times15-10=125\).
Since \(9x - 10=y - 20\) (corresponding angles), then \(y=9x-10 + 20\). Substitute \(x = 15\) into it:

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Answer:

\(x = 15\), \(y = 145\)