Question

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

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(v\), \(54^{\circ}\), and \(72^{\circ}\). Then the equation is \(v + 54+72=180\).

Step2: Solve the equation for \(v\)

Simplify the left - hand side of the equation: \(v+126 = 180\).
Subtract 126 from both sides of the equation: \(v=180 - 126\).

Answer:

\(v = 54^{\circ}\)