Write True or False and give reasons for your answer.
$A$ triangle $ABC$ can be constructed in which $\angle B = 60^{\circ}$,$\angle C = 45^{\circ}$ and $AB + BC + AC = 12 \text{ cm}$.

(TRUE) The given statement is true.
In any triangle $ABC$,the sum of the angles must be $180^{\circ}$. Here,$\angle B + \angle C = 60^{\circ} + 45^{\circ} = 105^{\circ}$. Since $105^{\circ} < 180^{\circ}$,the third angle $\angle A = 180^{\circ} - 105^{\circ} = 75^{\circ}$ can be determined.
According to the construction rules for a triangle given its perimeter and two base angles,a triangle can be constructed if the sum of the two base angles is less than $180^{\circ}$. Since $105^{\circ} < 180^{\circ}$,the construction is possible.