Question

if ( l parallel m ), find the values of ( x ) and ( y ) show all work on paper to receive partial credit ( (5y - 23)^circ ) ( (2x + 13)^circ ) ( (3x)^circ ) ( 47^circ ) ( l ) ( m ) ( x = ) ( y = )

Explanation:

Step1: Find the value of \(x\)

Since \(l\parallel m\), we use the property that the sum of the interior angle on the same - side of the transversal is \(180^{\circ}\).
The angle \((2x + 13)^{\circ}\) and \((3x)^{\circ}\) and \(47^{\circ}\) are related as \((2x+13)+(3x)+47 = 180\) (because they form a linear - like relationship for parallel lines \(l\) and \(m\) with a transversal).
Combine like terms: \(2x+3x+13 + 47=180\), so \(5x+60 = 180\).
Subtract 60 from both sides: \(5x=180 - 60\), \(5x=120\).
Divide both sides by 5: \(x=\frac{120}{5}=24\).

Step2: Find the value of \(y\)

We know that the angle \((5y - 23)^{\circ}\) and \((3x)^{\circ}\) are corresponding angles (since \(l\parallel m\)).
Substitute \(x = 24\) into \((3x)^{\circ}\), we get \(3x=3\times24 = 72^{\circ}\).
Set up the equation for \(y\): \(5y-23=72\).
Add 23 to both sides: \(5y=72 + 23\), \(5y=95\).
Divide both sides by 5: \(y=\frac{95}{5}=19\).

Answer:

\(x = 24\), \(y = 19\)