Answer:
∠ Y = 34°
Step-by-step explanation:
Since XY = ZY then the triangle is isosceles and the base angles are congruent, thus
∠ X = ∠ Y , that is
6x - 23 = 4x + 9 ( subtract 4x from both sides )
2x - 23 = 9 ( add 23 to both sides )
2x = 32 ( divide both sides by 2 )
x = 16
Thus
∠ Z = 4x + 9 = 4(16) + 9 = 64 + 9 = 73° = ∠ X
Hence
vertex angle Y = 180° - (73 + 73)° = 180° - 146° = 34°