The triangle in the image is an equilateral triangle, as indicated by the equal-length sides denoted by the tick marks on each side. In an equilateral triangle, all three interior angles are equal.

Since the sum of the interior angles of any triangle is $180^\circ$, each angle in an equilateral triangle is:

$\text{Angle} = \frac{180^\circ}{3} = 60^\circ$

Therefore, the measure of angle $x$ at vertex $Q$ is $60^\circ$.

Would you like any further details or have any questions?

Here are some related questions to consider:

1. What is the general formula for the sum of the interior angles of a polygon?
2. How do you calculate the exterior angles of an equilateral triangle?
3. What are the properties of an isosceles triangle compared to an equilateral triangle?
4. Can an equilateral triangle have an obtuse angle?
5. What is the formula for calculating the area of an equilateral triangle given the side length?

Tip: Remember that in any equilateral triangle, not only are all the angles equal, but so are all the sides. This is a key property that can help in solving various geometric problems related to triangles.