Question

1. find $m\angle b$.

Explanation:

Step1: Identify parallel side property

Since $\overrightarrow{AB} \parallel \overrightarrow{DC}$, consecutive interior angles are supplementary: $m\angle B + m\angle C = 180^\circ$

Step2: Substitute angle expressions

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

Step3: Simplify and solve for $x$

Combine like terms: $14x - 2 = 180$
Add 2 to both sides: $14x = 182$
Divide by 14: $x = \frac{182}{14} = 13$

Step4: Calculate $m\angle B$

Substitute $x=13$ into $9x+2$: $9(13) + 2 = 117 + 2$

Answer:

$119^\circ$