Find the measure of angle Q

This is an isosceles triangle. By the isosceles triangle theorem, if 2 sides are congruent to one another, then the angles opposite those sides are also congruent to one another. That means that angles P and R are equal. Therefore, we can set them equal to each other, solve for x, plug x back in and solve for the angle value. All triangles, regardless of what type they are, have angles that add up to equal 180. That means that

∠P + ∠Q + ∠R = 180°

Setting P and R equal to each other:

2x + 10 = 6x - 4.

Combining like terms:

14 = 4x so

x = 7/2.

Sub that back into P to find the angle measure of P (and R also, since they are the same):

∠P = 2(7/2) + 10

∠P = 17 so

∠R = 17

If the angles add up to 180, then

∠Q = 180 - 17 - 17 so

∠Q = 146°