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, \((v - 46^{\circ})+(v - 38^{\circ})+40^{\circ}=180^{\circ}\).

Step2: Combine like - terms

First, simplify the left - hand side of the equation: \((v + v)+(-46^{\circ}-38^{\circ}+40^{\circ})=180^{\circ}\), which gives \(2v+(-44^{\circ}) = 180^{\circ}\), or \(2v-44^{\circ}=180^{\circ}\).

Step3: Isolate the variable \(v\)

Add 44° to both sides of the equation: \(2v=180^{\circ}+44^{\circ}\), so \(2v = 224^{\circ}\). Then divide both sides by 2: \(v=\frac{224^{\circ}}{2}\).

Answer:

\(v = 112^{\circ}\)