what is the value of v?

Answer:

$70^{\circ}$

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is $360^{\circ}$, and vertical angles are equal. Also, we can use the fact that the sum of angles on one - side of a straight - line is $180^{\circ}$. Consider the angles $30^{\circ}$ and $40^{\circ}$ and the angle $v$. The sum of the angles adjacent to $v$ on one side of the straight - line formed by the intersection of the lines is $30^{\circ}+40^{\circ}=70^{\circ}$.

Step2: Calculate the value of $v$

Since the sum of angles on one side of a straight - line is $180^{\circ}$, and the non - $v$ part of the straight - line is $70^{\circ}$, then $v = 180^{\circ}-(30^{\circ}+40^{\circ})=70^{\circ}$.