Question

in the figure below, ( mparallel n ). find the values of ( x ) and ( y ).
note: the figure is not drawn to scale.
( x = 123,y = 25.2 )
( x = 57,y = 12 )
( x = 123,y = 12 )
( x = 57,y = 25.2 )

Explanation:

Step1: Find the value of \(x\)

Since \(m\parallel n\), \(x\) and \(123^{\circ}\) are supplementary angles (consecutive interior angles).
\(x + 123^{\circ}=180^{\circ}\)
\(x=180^{\circ}- 123^{\circ}\)
\(x = 57^{\circ}\)

Step2: Find the value of \(y\)

\(x\) and \((5y - 3)^{\circ}\) are vertical angles. So \(x=(5y - 3)^{\circ}\)
Substitute \(x = 57\) into the equation:
\(57=5y-3\)
Add \(3\) to both sides:
\(57 + 3=5y\)
\(60 = 5y\)
Divide both sides by \(5\):
\(y=\frac{60}{5}\)
\(y = 12\)

Answer:

\(x = 57,y = 12\) (the second option)