In ΔABC, mÐA = 40, mÐB = 70, and AC = 5 centimeters. Find the
length of AB in centimeters.
Since $\displaystyle m\angle A=40^{\circ}, m \angle B=70^{\circ}$, it follows that $\displaystyle m\angle C=70^{\circ}$ since the sum of the measures of the angles of a triangle is 180 degrees.
If two angles of a triangle are congruent, then the triangle is isosceles.
If the triangle is isosceles then the sides opposite the congruent angles are congruent.
$\displaystyle \angle B \cong \angle C \rightarrow \overline{AC} \cong \overline{AB}$
$\displaystyle AC = AB = 5$cm.