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, \(4x - 10=8x - 2\).
\[

$$\begin{align*} 4x-10&=8x - 2\\ 4x-8x&=- 2 + 10\\ -4x&=8\\ x&=-2 \end{align*}$$

\]
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).
\[

$$\begin{align*} 4x-10+8x - 2&=180\\ 12x-12&=180\\ 12x&=180 + 12\\ 12x&=192\\ x&=16 \end{align*}$$

\]

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:

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