Question

1. directions: if ( l parallel m ), solve for ( x ) and ( y ).

Explanation:

Step1: Solve for \(x\)

Since \(l\parallel m\), the corresponding angles are equal. So, \(13x - 19=9x + 25\).
Subtract \(9x\) from both sides: \(13x-9x-19 = 9x - 9x+25\), which gives \(4x-19=25\).
Add \(19\) to both sides: \(4x-19 + 19=25 + 19\), so \(4x=44\).
Divide both sides by \(4\): \(x=\frac{44}{4}=11\).

Step2: Solve for \(y\)

The angles \((13x - 19)^{\circ}\) and \((17y + 5)^{\circ}\) are supplementary (they form a linear pair).
First, substitute \(x = 11\) into \(13x-19\): \(13\times11-19=143 - 19 = 124\).
Then, since \(124+(17y + 5)=180\) (supplementary angles sum to \(180^{\circ}\)).
Simplify the left - hand side: \(17y+129 = 180\).
Subtract \(129\) from both sides: \(17y+129 - 129=180 - 129\), so \(17y = 51\).
Divide both sides by \(17\): \(y=\frac{51}{17}=3\).

Answer:

\(x = 11\) and \(y = 3\)