Question

the diagram shows a triangle. what is the value of v? v =

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180°. So, \((v + 9)+(4v+9)+(3v - 6)=180\).

Step2: Combine like - terms

\(v+4v + 3v+9 + 9-6=180\), which simplifies to \(8v+12 = 180\).

Step3: Isolate the variable term

Subtract 12 from both sides: \(8v=180 - 12\), so \(8v=168\).

Step4: Solve for v

Divide both sides by 8: \(v=\frac{168}{8}=21\).

Answer:

21