Question

directions: if ( lparallel m ), solve for ( x ) and ( y ).

Explanation:

Step1: Use corresponding - angles property for x

Since \(l\parallel m\), corresponding angles are equal. For the x - related angles in problem 9, we have \(13x - 19=9x + 25\).
\[

$$\begin{align*} 13x-9x&=25 + 19\\ 4x&=44\\ x& = 11 \end{align*}$$

\]

Step2: Use corresponding - angles property for y in problem 9

For the y - related angles in problem 9, we use the fact that corresponding angles are equal. So \(17y+5=(13x - 19)\). Substitute \(x = 11\) into the equation: \(17y+5=13\times11-19\).
\[

$$\begin{align*} 17y+5&=143-19\\ 17y+5&=124\\ 17y&=119\\ y& = 7 \end{align*}$$

\]

Step3: Use corresponding - angles property for x in problem 10

Since \(l\parallel m\), corresponding angles are equal. So \(3x-29=6x - 7\).
\[

$$\begin{align*} 6x-3x&=-29 + 7\\ 3x&=-22\\ x&=-\frac{22}{3} \end{align*}$$

\]

Step4: Use corresponding - angles property for y in problem 10

For the y - related angles in problem 10, we have \(8y + 17=3x-29\). Substitute \(x=-\frac{22}{3}\) into the equation:
\[

$$\begin{align*} 8y+17&=3\times(-\frac{22}{3})-29\\ 8y+17&=-22-29\\ 8y+17&=-51\\ 8y&=-68\\ y&=-\frac{17}{2} \end{align*}$$

\]
In problem 9:

Answer:

\(x = 11,y = 7\)
In problem 10:
\(x=-\frac{22}{3},y =-\frac{17}{2}\)