Question

Will give Brainlyest! Find the measure of the vertex angle.

Answer 1

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°