Question

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

Explanation:

Step1: Find the value of \( x \)

Since \( m \parallel n \), the alternate - interior angles are equal. The angle with measure \( 47^{\circ} \) and \( x^{\circ} \) are alternate - interior angles. So \( x = 47 \).

Step2: Find the value of \( y \)

We know that \( x \) and \( y \) are supplementary angles (they form a linear pair), which means \( x + y=180^{\circ} \).
We already found that \( x = 47 \), so substitute \( x = 47 \) into the equation \( 47 + y=180 \).
To solve for \( y \), we subtract 47 from both sides of the equation: \( y=180 - 47=133 \).

Answer:

\( x = 47 \), \( y = 133 \)