Construct the following angle and verify by measuring it with a protractor: $75^{\circ}$

(N/A) $75^{\circ} = 60^{\circ} + 15^{\circ}$
Steps of construction:
$I.$ Draw a ray $\overrightarrow{ OA }$.
$II.$ With $O$ as the center and a suitable radius,draw an arc that meets $\overrightarrow{ OA }$ at $B$.
$III.$ With center $B$ and the same radius,mark a point $C$ on the previous arc. Now,$\angle BOC = 60^{\circ}$.
$IV.$ With center $C$ and the same radius,mark another point $D$ on the arc. Now,$\angle COD = 60^{\circ}$.
$V.$ Draw $\overrightarrow{ OP }$,the bisector of $\angle COD$,such that $\angle COP = \frac{1}{2}(60^{\circ}) = 30^{\circ}$. Thus,$\angle BOP = 60^{\circ} + 30^{\circ} = 90^{\circ}$.
$VI.$ Draw $\overrightarrow{ OQ }$,the bisector of $\angle COP$,such that $\angle COQ = 15^{\circ}$.
Thus,$\angle BOQ = \angle BOC + \angle COQ = 60^{\circ} + 15^{\circ} = 75^{\circ}$.
Finally,verify the angle using a protractor.