Question

9 = (13x - 19)° (9x + 25)° (17y + 5)°

Explanation:

Step1: Use the property of parallel lines

Since \( l\parallel m\), the corresponding angles are equal. So \(13x - 19=9x + 25\).

Step2: Solve the equation for \(x\)

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 \(4\): \(x=\frac{44}{4}=11\).

Step3: Use the property of vertical angles

The angles \((13x - 19)^{\circ}\) and \((17y + 5)^{\circ}\) are vertical angles. Substitute \(x = 11\) into \(13x-19\): \(13\times11-19=143 - 19=124\).
So \(17y+5 = 124\).

Step4: Solve the equation for \(y\)

Subtract \(5\) from both sides: \(17y+5 - 5=124 - 5\), which gives \(17y=119\).
Divide both sides by \(17\): \(y=\frac{119}{17}=7\).

Answer:

\(x = 11,y = 7\)