Question

what is the value of \x\ and what is the measure of \\( \angle wql \\)?

Explanation:

Step1: Use the angle - sum property

Since \(\angle WQK=(13x + 4)^{\circ}\) and \(\angle KQL = 9x^{\circ}\) and \(\angle WQK+\angle KQL=180^{\circ}\) (linear pair of angles), we have the equation \((13x + 4)+9x=180\).

Step2: Simplify the equation

Combine like terms: \(13x+9x+4 = 180\), which gives \(22x+4=180\).
Subtract 4 from both sides: \(22x=180 - 4\), so \(22x=176\).
Divide both sides by 22: \(x=\frac{176}{22}=8\).

Step3: Find the measure of \(\angle WQL\)

Substitute \(x = 8\) into \(\angle WQL=(13x + 4)^{\circ}\).
\(\angle WQL=(13\times8+4)^{\circ}=(104 + 4)^{\circ}=108^{\circ}\).

Answer:

\(x = 8\) and the measure of \(\angle WQL\) is \(108^{\circ}\)