Question

1. find $m\angle cbf$.

corresponding $\cong$
$\angle cbf=(9x + 2)^\circ$
$\angle dfe=(15x - 52)^\circ$

Explanation:

Step1: Set angles equal (corresponding)

Since $\angle CBF$ and $\angle DFE$ are corresponding angles, they are congruent:
$9x + 2 = 15x - 52$

Step2: Solve for $x$

Rearrange to isolate $x$:
$2 + 52 = 15x - 9x$
$54 = 6x$
$x = \frac{54}{6} = 9$

Step3: Substitute $x$ into angle formula

Plug $x=9$ into $\angle CBF = 9x + 2$:
$\angle CBF = 9(9) + 2$

Answer:

$83^\circ$