The measures of the angles in a triangle add up to 180°.
[tex]m \angle A + m \angle B + m \angle C = 180^\circ \\
m \angle A=43^\circ, \ m \angle C = 66^\circ \\ \downarrow \\
43^\circ+ m \angle B + 66^\circ = 180^\circ \\
m \angle B + 109^\circ = 180^\circ \\
m \angle B =180^\circ - 109^\circ \\
\boxed{m \angle B=71^\circ}[/tex]
