Question

solve for the value of q.

Explanation:

Step1: Recall angle - sum property

The sum of the three angles is 180 degrees. So, \((4q - 5)+90+(5q + 5)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(4q-5 + 90+5q + 5=4q+5q+( - 5+5 + 90)=9q + 90\). So, \(9q+90 = 180\).

Step3: Isolate the variable term

Subtract 90 from both sides: \(9q+90-90=180 - 90\), which gives \(9q=90\).

Step4: Solve for q

Divide both sides by 9: \(\frac{9q}{9}=\frac{90}{9}\), so \(q = 10\).

Answer:

\(q = 10\)