Question

find the value of x so that k || m. simplify your answer as much as possible. (4x + 13)° (5x + 14)°

Explanation:

Step1: Use the property of same - side interior angles

When \(k\parallel m\), the sum of same - side interior angles is \(180^{\circ}\). So, \((4x + 13)+(5x + 14)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+5x+13 + 14=180\), which gives \(9x+27 = 180\).

Step3: Isolate the term with \(x\)

Subtract \(27\) from both sides: \(9x=180 - 27\), so \(9x=153\).

Step4: Solve for \(x\)

Divide both sides by \(9\): \(x=\frac{153}{9}\).

Answer:

\(x = 17\)