The image you provided shows a geometry problem involving angles and asks to solve for $x$. There are three angles given in terms of $x$:

1. $2x + 10^\circ$
2. $4x - 5^\circ$
3. $3x$

These angles are arranged around a point on a straight line. Since the angles on a straight line sum up to $180^\circ$, we can form the equation:

$(2x + 10^\circ) + (4x - 5^\circ) + 3x = 180^\circ$

Let's solve this equation step by step.

1. Combine like terms: $2x + 4x + 3x + 10^\circ - 5^\circ = 180^\circ$ $9x + 5^\circ = 180^\circ$

2. Subtract $5^\circ$ from both sides: $9x = 175^\circ$

3. Divide by 9 to solve for $x$: $x = \frac{175}{9} \approx 19.44^\circ$

So, $x \approx 19.44^\circ$.

Let me know if you need further clarification or a detailed breakdown!

Related questions:

1. What would happen if the angles added up to more or less than $180^\circ$?
2. Can you verify the angle sum by substituting $x$ back into the original expressions?
3. What happens if the equation was set up around a different type of angle, such as a right angle?
4. How does this technique extend to three-dimensional problems?
5. What are alternate methods to approach the same type of angle problem?

Tip:

Always remember to check that the angles sum up to a correct total, especially in problems involving lines and points!