Question

the shape abcd below is an isosceles trapezoid. what is the measure of ∠b? (note that the figure is not drawn to scale.)

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal and adjacent angles along non - parallel sides are supplementary. $\angle A$ and $\angle D$ are adjacent angles along non - parallel sides, and $\angle B$ and $\angle C$ are adjacent angles along non - parallel sides. Also, $\angle A+\angle D = 180^{\circ}$ and $\angle B+\angle C=180^{\circ}$, and $\angle A=\angle B$, $\angle C = \angle D$.

Step2: Use the supplementary - angle relationship

We know that $\angle D = 81^{\circ}$. Since $\angle B$ and $\angle D$ are supplementary (because $AB\parallel CD$ in trapezoid $ABCD$), we use the formula $\angle B+\angle D=180^{\circ}$.
Let $\angle B=x$. Then $x + 81^{\circ}=180^{\circ}$.
Solve for $x$: $x=180^{\circ}-81^{\circ}$.
$x = 99^{\circ}$.

Answer:

$99^{\circ}$