Question

given m || n, find the value of x and y. (4x - 10)° m (8x - 2)° (2y)° n

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(4x - 10=8x - 2\).

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This is incorrect. We should use the property of alternate - exterior angles. The alternate - exterior angles formed by parallel lines \(m\) and \(n\) are equal. So \(4x-10 + 8x - 2=180\) (because they are supplementary).

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Step2: Find the value of \(y\)

We know that \(8x-2\) and \(2y\) are vertical angles. Vertical angles are equal.
First, substitute \(x = 16\) into \(8x-2\): \(8\times16-2=128 - 2=126\).
Since \(8x - 2=2y\), then \(2y=126\), and \(y = 63\).

Answer:

\(x = 16\), \(y = 63\)