In the image, we have two angles on a straight line. One angle is $30^\circ$, and the other angle is labeled as $(3x)^\circ$. Since these two angles are on a straight line, they are supplementary, meaning their sum equals $180^\circ$.

We can set up the equation as follows:

$30^\circ + (3x)^\circ = 180^\circ$

Now, solve for $x$:

1. Subtract 30 from both sides:

$3x = 180^\circ - 30^\circ$

$3x = 150^\circ$

2. Divide both sides by 3:

$x = \frac{150^\circ}{3} = 50^\circ$

So, $x = 50^\circ$.

Would you like any further explanation or details?

5 Related Questions:

1. What are supplementary angles, and how are they used in solving equations?
2. How would the problem change if the given angle were different, say $40^\circ$?
3. Can this method be applied to non-straight angles, like interior angles of polygons?
4. How do you find the value of $x$ if both angles had variable expressions?
5. What are complementary angles, and how are they different from supplementary ones?

Tip:

When dealing with angles on a straight line, always remember they must sum up to $180^\circ$. This is a useful fact in geometry problems!