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, \(47^{\circ}+31^{\circ}+17v = 180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add \(47^{\circ}\) and \(31^{\circ}\): \(47 + 31=78\). The equation becomes \(78+17v = 180\).

Step3: Solve for \(v\)

Subtract \(78\) from both sides: \(17v=180 - 78\). Then \(17v = 102\). Divide both sides by \(17\): \(v=\frac{102}{17}\).

Answer:

\(v = 6\)