Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we have the equation \(30+(2v - 19)+31 = 180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \(30-19 + 31+2v=180\).
\((30 + 31-19)+2v=180\), \(42 + 2v=180\).

Step3: Isolate the variable term

Subtract 42 from both sides of the equation: \(2v=180 - 42\).
\(2v=138\).

Step4: Solve for \(v\)

Divide both sides by 2: \(v=\frac{138}{2}\).
\(v = 69\).

Answer:

69