Answer
The base angle is $\approx 68^{\circ}$.
Work Step by Step
1. Use the Law of Cosines
$c^{2} = a^{2} + b^{2} - 2abcos(C)$
$(30)^{2} = (40)^{2} + (40)^{2} - 2(40)(40)cos(C)$
$900 = 1600 + 1600 - 3200cos(C)$
$900 = 3200 - 3200cos(C)$
$-2300 = -3200cos(C)$
$cos(C) = 0.71875$
by GDC / calculator
$C = 44.0486...^{\circ}$
2. Find one of the base angles knowing that angles in a $\triangle$ add to $180^{\circ}$
$= \frac{180-(44.0486...)}{2}$
$= 67.975...^{\circ}$
$\approx 68^{\circ}$
