Write True or False and give reasons for your answer.
An angle of $52.5^{\circ}$ can be constructed.

(A) To determine if an angle of $52.5^{\circ}$ can be constructed,we check if it is a multiple of $7.5^{\circ}$,as angles that are multiples of $7.5^{\circ}$ can be constructed using a compass and ruler.
We can express $52.5^{\circ}$ as:
$52.5^{\circ} = \frac{105^{\circ}}{2} = \frac{1}{2} \times (60^{\circ} + 45^{\circ})$.
Since $60^{\circ}$ and $45^{\circ}$ are standard angles that can be constructed,their sum $105^{\circ}$ can be constructed. By bisecting the $105^{\circ}$ angle,we obtain $52.5^{\circ}$.
Alternatively,$52.5^{\circ} = \frac{210^{\circ}}{4} = \frac{180^{\circ} + 30^{\circ}}{4}$. Since $180^{\circ}$ and $30^{\circ}$ are constructible,$210^{\circ}$ is constructible,and bisecting it twice yields $52.5^{\circ}$.
Therefore,the statement is True.