Find the measure of angle Q

Answer:146°Step-by-step explanation: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 sox = 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 = 17If the angles add up to 180, then∠Q = 180 - 17 - 17 so∠Q = 146°