3. The measure of two vertical angles are given by the expressions $(x+3)^{\circ}$ and $(2 x-7)^{\circ}$. Find the value of $x$. What is the measure of each angle?

Step 1 ：The problem is asking for the value of x and the measure of each angle. Vertical angles are angles opposite each other when two lines intersect. They are always equal. So, we can set the two expressions equal to each other and solve for x. After finding the value of x, we can substitute it back into the expressions to find the measure of each angle.

Step 2 ：Set the two expressions equal to each other: \((x+3)^{\circ} = (2x-7)^{\circ}\)

Step 3 ：Solve for x to get \(x = 10\)

Step 4 ：Substitute x = 10 back into the expressions to find the measure of each angle: \((10+3)^{\circ} = 13^{\circ}\) and \((2*10-7)^{\circ} = 13^{\circ}\)

Step 5 ：Final Answer: The value of x is \(\boxed{10}\) and the measure of each angle is \(\boxed{13^{\circ}}\)