Set up equations based on problem

Since AC = BC, the angles opposite to these sides are equal, so $\angle A = \angle B$. Let the angles be $\angle A = \angle B = x$ and $\angle C = y$. The sum of angles in a triangle is $180°$, so $2x + y = 180$. From the problem, $x = \frac{2}{5}y - 9$.

$2x + y = 180, x = \frac{2}{5}y - 9$

Solve for the angles

Substitute $x$ into the sum equation: $2(\frac{2}{5}y - 9) + y = 180$. This simplifies to $\frac{4}{5}y - 18 + y = 180$, or $\frac{9}{5}y = 198$. Solving for $y$, we get $y = 198 \times \frac{5}{9} = 22 \times 5 = 110°$. Thus, $x = \frac{2}{5}(110) - 9 = 44 - 9 = 35°$.

$y = 110°, x = 35°$

Evaluate the final expression

We need to find the value of $\frac{2\angle C - 3\angle A + \angle B}{2}$. Substituting the values $\angle C = 110°$, $\angle A = 35°$, and $\angle B = 35°$: $\frac{2(110) - 3(35) + 35}{2} = \frac{220 - 105 + 35}{2} = \frac{150}{2} = 75°$.

$\frac{220 - 105 + 35}{2} = 75°$