Question

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

Explanation:

Step1: Find the value of \( y \)

Since \( y^{\circ} \) and \( 43^{\circ} \) are supplementary angles (they form a linear pair), we use the formula \( y + 43=180 \).
Subtracting 43 from both sides gives \( y = 180 - 43 \).

Step2: Find the value of \( x \)

Because \( m\parallel n \), \( x^{\circ} \) and \( 43^{\circ} \) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \( x = 43 \).

Answer:

\( x = 43 \), \( y = 137 \)