Question

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

Explanation:

Step1: Use the triangle angle - sum property

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

Step2: Simplify the left - hand side of the equation

Combine like terms: \(v+30 + 2v+2v=(1 + 2+2)v+30=5v + 30\). The equation becomes \(5v+30 = 180\).

Step3: Solve for \(v\)

Subtract 30 from both sides: \(5v+30-30=180 - 30\), which gives \(5v=150\). Then divide both sides by 5: \(v=\frac{150}{5}\).

Answer:

\(v = 30\)