Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \(6v + 6v+72^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(12v + 72^{\circ}=180^{\circ}\).

Step3: Isolate the term with \(v\)

Subtract \(72^{\circ}\) from both sides: \(12v=180^{\circ}-72^{\circ}\). Then \(12v = 108^{\circ}\).

Step4: Solve for \(v\)

Divide both sides by \(12\): \(v=\frac{108^{\circ}}{12}\).

Answer:

\(v = 9\)