Question

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

Explanation:

Step1: Find the value of \( x \)

Since \( x \) and \( 51^{\circ} \) are supplementary angles (they form a linear pair), we use the formula \( x + 51^{\circ}=180^{\circ} \).

$$ x = 180^{\circ}- 51^{\circ} $$

$$ x = 129^{\circ} $$

Step2: Find the value of \( y \)

Since \( y \) and \( 51^{\circ} \) are alternate - interior angles (because \( m\parallel n \)), so \( y = 51^{\circ} \).

Answer:

\( x = 129 \), \( y = 51 \)