The triangle in the image is an isosceles triangle, as indicated by the two equal angle marks at the base.

We are given that:

• The top angle is $3x^\circ$.
• The two base angles are $4x^\circ$ each.

In a triangle, the sum of all interior angles must equal 180°. Therefore, we can set up the equation:

$3x + 4x + 4x = 180^\circ$

Simplifying this:

$11x = 180^\circ$

Now, solve for $x$:

$x = \frac{180^\circ}{11} \approx 16.36^\circ$

Thus, $x \approx 16.36^\circ$.

Would you like further clarification or more details on the steps?

Here are 5 related questions:

1. How do you find the angles in an equilateral triangle?
2. Can you explain how the exterior angle of a triangle relates to interior angles?
3. What is the sum of interior angles in a polygon with $n$ sides?
4. How would you solve a triangle if one angle is given and two sides are known?
5. What defines an isosceles triangle mathematically?

Tip: Remember, in any triangle, the sum of the interior angles is always 180°. This can be a helpful shortcut for solving problems like this one!