Since the two angles are vertical angles, they are congruent. This means they are equal in measure.

The given information states that:

• One angle measures 145°.
• The other angle measures $2x + 5$.

Since these two angles are congruent, we can set up the following equation:

$145 = 2x + 5$

Now, solve for $x$:

1. Subtract 5 from both sides: $145 - 5 = 2x$ $140 = 2x$

2. Divide both sides by 2: $\frac{140}{2} = x$ $x = 70$

So, the value of $x$ is $\boxed{70}$.

Would you like more details on this, or do you have any other questions? Here are some follow-up questions you might find helpful:

1. What are some other examples of vertical angles?
2. How do you know when two angles are congruent?
3. What happens if the angles are not vertical?
4. Can vertical angles ever be complementary or supplementary?
5. How does this problem apply to real-world situations like architecture or engineering?

Tip: Always remember that vertical angles are equal, which can often simplify equations in geometry problems.