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, \(56+(v + 2)+(v-20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(56+v + 2+v-20=(56 + 2-20)+(v + v)=38 + 2v\).
The equation becomes \(38+2v=180\).

Step3: Solve for \(v\)

Subtract 38 from both sides: \(2v=180 - 38\), so \(2v=142\).
Divide both sides by 2: \(v=\frac{142}{2}\).

Answer:

\(v = 71\)