Question

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

Explanation:

Step1: Find the value of \( x \)

Since \( x^\circ \) and \( 51^\circ \) are supplementary angles (they form a linear pair), their sum is \( 180^\circ \). So we have the equation \( x + 51 = 180 \). Solving for \( x \), we subtract \( 51 \) from both sides: \( x = 180 - 51 = 129 \).

Step2: Find the value of \( y \)

Since \( m \parallel n \), the angle \( y^\circ \) and the \( 51^\circ \) angle are alternate - interior angles. By the alternate - interior angles theorem, alternate - interior angles are equal when two parallel lines are cut by a transversal. So \( y = 51 \).

Answer:

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