Question

what is the value of v?

Explanation:

Step1: Recall the property of isosceles triangle

In \(\triangle ABC\), since \(AB = BC\) (marked by the same tick - marks), \(\triangle ABC\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle A=\angle C = v\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle ABC\), we have \(\angle A+\angle B+\angle C = 180^{\circ}\). Substituting \(\angle A = v\), \(\angle B=56^{\circ}\) and \(\angle C = v\) into the formula, we get the equation \(v + 56^{\circ}+v=180^{\circ}\).

Step3: Solve the equation for \(v\)

Combine like terms: \(2v+56^{\circ}=180^{\circ}\). Subtract \(56^{\circ}\) from both sides of the equation: \(2v=180^{\circ}- 56^{\circ}\). So \(2v = 124^{\circ}\). Divide both sides by 2: \(v=\frac{124^{\circ}}{2}\).

Answer:

\(62\)