Question

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

Step1: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(3v + 35^{\circ}+115^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add \(35^{\circ}\) and \(115^{\circ}\): \(3v+(35 + 115)^{\circ}=180^{\circ}\), which gives \(3v + 150^{\circ}=180^{\circ}\).

Step3: Solve for \(v\)

Subtract \(150^{\circ}\) from both sides: \(3v=180^{\circ}-150^{\circ}\), so \(3v = 30^{\circ}\). Then divide both sides by \(3\): \(v=\frac{30^{\circ}}{3}\).

Answer:

\(v = 10\)