Question

1. if ( l parallel m ), find the value of each missing variable(s).

( (6 x-7)^{circ} )
( (3 x-29)^{circ} )
( x = 7 y = 3 )
( x = 17 y = 4 )
( x = 24 y = 15 )

Explanation:

Step1: Use the property of parallel lines (corresponding angles)

Since \(l\parallel m\), the angles \((6x - 7)^{\circ}\) and \((3x+29)^{\circ}\) are congruent (corresponding angles). So, \(6x-7 = 3x + 29\).
Subtract \(3x\) from both sides: \(6x-3x-7=3x - 3x+29\), which gives \(3x-7 = 29\).
Add \(7\) to both sides: \(3x-7 + 7=29 + 7\), so \(3x=36\).
Divide both sides by \(3\): \(x=\frac{36}{3}=12\) (Wait, no, let's re - check. Wait, actually, if \(l\parallel m\), \((6x - 7)\) and \((3x-29)\) are same - side interior angles? No, no. Wait, \((6x - 7)\) and \((3x-29)\) are actually supplementary (same - side interior angles). Wait, no, no. Wait, if \(l\parallel m\), \((6x - 7)\) and \((3x-29)\) are same - side interior angles. So \(6x-7+3x - 29=180\).
Combine like terms: \(9x-36 = 180\).
Add \(36\) to both sides: \(9x=180 + 36=216\).
Divide by \(9\): \(x = 24\).

Step2: Use the property of vertical angles

The angle \((8y + 17)\) is equal to \((6x - 7)\). Substitute \(x = 24\) into \(6x-7\): \(6\times24-7=144 - 7=137\).
So \(8y+17 = 137\).
Subtract \(17\) from both sides: \(8y=137 - 17 = 120\).
Divide by \(8\): \(y=\frac{120}{8}=15\).

Answer:

\(x = 24,y = 15\)