Question

the diagram shows a triangle. what is the value of v? write your answer as an integer or as a decimal rounded to the nearest tenth. v =

Explanation:

Step1: Use the triangle angle sum theorem

The sum of interior angles in a triangle is \(180^{\circ}\). So, \((v - 12)+(2v - 8)+30=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((v+2v)+(-12 - 8 + 30)=180\), which is \(3v+(10)=180\), or \(3v+10 = 180\).

Step3: Solve for \(v\)

Subtract \(10\) from both sides: \(3v=180 - 10\), so \(3v=170\). Then divide both sides by \(3\): \(v=\frac{170}{3}\approx56.7\).

Answer:

\(v = 56.7\)