Copy $\angle AOB$ shown in the given figure. Using a ruler and compass, construct an angle equal to $2\frac{1}{2}$times $\angle AOB$.

Given $\overline{AB}$ of length $3.9 \mathrm{cm}$, construct $\overline{PQ}$ such that the length of $\overline{PQ}$ is twice that of $\overline{AB}$. Verify by measurement.

[Hint: Construct $\overline{PX}$ such that length of $PX=$length of $\overline{AB}$; then cut off $\overline{XQ}$ such that $\overline{XQ}$ also has the length of $\overline{AB}$.]