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, \(31^{\circ}+(v - 42)^{\circ}+119^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((31 + v-42 + 119)^{\circ}=180^{\circ}\).
\((v+(31 - 42+119))^{\circ}=180^{\circ}\).
\((v + 108)^{\circ}=180^{\circ}\).

Step3: Solve for \(v\)

Subtract \(108^{\circ}\) from both sides of the equation: \(v=180 - 108\).

Answer:

\(72\)