Question

if ( l parallel m ), find the value of ( x ) and the value of ( y ).
a. ( x = 75, y = 60 )
b. ( x = 82, y = 53 )
c. ( x = 90, y = 45 )
d. ( x = 95, y = 40 )
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Explanation:

Step1: Find the value of \(x\)

Since \(l\parallel m\), the angle \((2x - 30)^{\circ}\) and \((x + 45)^{\circ}\) are equal (corresponding angles).
\(2x-30=x + 45\)
\(2x-x=45 + 30\)
\(x = 75\)

Step2: Find the value of \(y\)

We know that \(x+y+45^{\circ}=180^{\circ}\) (straight - line angle). Substitute \(x = 75\) into the equation:
\(75+y+45=180\)
\(y+120=180\)
\(y=180 - 120\)
\(y = 60\)

Answer:

A. \(x = 75,y = 60\)