Question

fill in the blank 1 point

1. find ( mangle b ).

( mangle b = ) type your answer...

Explanation:

Step1: Identify consecutive interior angles

Since $AB \parallel DC$, $\angle B$ and $\angle C$ are consecutive interior angles, so their sum is $180^\circ$.
$$(9x + 2) + (5x - 4) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.
$$14x - 2 = 180$$
$$14x = 182$$
$$x = \frac{182}{14} = 13$$

Step3: Calculate $m\angle B$

Substitute $x=13$ into the expression for $\angle B$.
$$m\angle B = 9(13) + 2 = 117 + 2$$

Answer:

$119^\circ$