Write True or False and give reasons for your answer.
An angle of $67.5^{\circ}$ can be constructed.

(A) True.
An angle of $67.5^{\circ}$ can be constructed because it is half of $135^{\circ}$.
Since $135^{\circ} = 90^{\circ} + 45^{\circ}$,we can construct $90^{\circ}$ and $45^{\circ}$ using a compass and ruler.
By bisecting the angle of $135^{\circ}$,we obtain $67.5^{\circ}$ $(67.5^{\circ} = \frac{135^{\circ}}{2})$.
Therefore,the statement is true.