Question

$m\angle xyz = 130^\circ$. what is $m\angle wyx$?
$(6x - 4)^\circ$
$(9x - 16)^\circ$
a $20^\circ$
b $56^\circ$
c $65^\circ$
d $74^\circ$

Explanation:

Step1: Set up angle sum equation

$\angle XYZ = \angle XYW + \angle WYZ$
$130^\circ = (6x-4)^\circ + (9x-16)^\circ$

Step2: Simplify and solve for $x$

Combine like terms:
$130 = 15x - 20$
Add 20 to both sides:
$150 = 15x$
Divide by 15:
$x = 10$

Step3: Calculate $m\angle WYX$

Substitute $x=10$ into $(6x-4)$:
$m\angle WYX = 6(10) - 4$

Answer:

$\boldsymbol{56^\circ}$ (Option B. 56°)