Question

question
given ( m parallel n ), find the value of ( x ) and ( y ).
(image of two parallel lines ( m ) and ( n ) cut by a transversal, with angles ( x^circ ), ( y^circ ) on line ( m ) and ( 47^circ ) on line ( n ))

Explanation:

Step1: Find x using alternate interior angles

Since \( m \parallel n \) and the transversal creates alternate interior angles, \( x = 47^\circ \) (alternate interior angles are equal).

Step2: Find y using linear pair

\( x \) and \( y \) form a linear pair, so \( x + y = 180^\circ \). Substituting \( x = 47^\circ \), we get \( 47 + y = 180 \). Solving for \( y \), \( y = 180 - 47 = 133^\circ \).

Answer:

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