Find the measure of $\angle$ABC if AB = BC.

From Figure, $\angle BAC + \angle CAD = 180°$  (Linear Pair)
$\Rightarrow \angle BAC + 100° = 180°$
$\Rightarrow \angle BAC = 80°$
In Δ ABC, $\angle BAC = 80°$  (from the above equation)
and AB = BC  (Given)
$\Rightarrow \angle A = \angle C$  (Angles opposite to two equal sides of a triangle are equal)
$\angle BAC + \angle ABC + \angle ACB = 180°$  (Angle Sum property of triangle)
$\Rightarrow 80° + \angle B + 80° = 180°$
$\Rightarrow \angle B = 180° – 160°$
$\Rightarrow \angle B = 20°$