Using the triangle interior theorem,
All three interior angles of a triangle add up to 180.
So that means angle x+23+134=180
Since two angles have the same measure, that means there are two sides that have same measure. Using the converse of base angles theorem,
If two angles are congruent, then the sides opposite of those angles are congruent.
Since the given angle 23 is opposite of side y and our missing angle (which is 23) is opposite of the side that measures 15.
Side y measures 15.
This triangles is a obtuse isoceles triangle.