Question

1. solve for ( mangle b ).

options: ( 90^circ ), ( 110^circ ), ( 55^circ ), ( 70^circ )

Explanation:

Step1: Identify the quadrilateral type

The figure is an isosceles trapezoid: $\overline{AB} \parallel \overline{DC}$, $\overline{AD} = \overline{BC}$.

Step2: Use trapezoid angle property

Consecutive angles between parallel sides are supplementary: $m\angle B + m\angle C = 180^\circ$

Step3: Substitute known angle and solve

Substitute $m\angle C = 110^\circ$:
$m\angle B = 180^\circ - 110^\circ = 70^\circ$

Answer:

70°