Question

find x, $\angle b$, and $\angle c$
this is a most specifically a
$x = \square$
$\angle b = \square ^\circ$
$\angle c = \square ^\circ$

Explanation:

Step1: Use trapezoid consecutive angles property

$\angle B + \angle C = 180^\circ$

Step2: Substitute angle expressions

$(9x + 2) + (5x - 4) = 180$

Step3: Simplify and solve for x

$14x - 2 = 180$
$14x = 182$
$x = \frac{182}{14} = 13$

Step4: Calculate $\angle B$

$\angle B = 9(13) + 2 = 117 + 2 = 119$

Step5: Calculate $\angle C$

$\angle C = 5(13) - 4 = 65 - 4 = 61$

Answer:

This is a most specifically a trapezoid
$x = 13$
$\angle B = 119^\circ$
$\angle C = 61^\circ$