1. **Problem:** Draw an angle and label it as $\angle BAC$. Construct another angle equal to $\angle BAC$. 2. **Formula and rules:** To construct an angle equal to a given angle, we use the compass to copy the arc and the length between the intersection points on the rays. 3. **Steps:** - Construct $\angle BAC$ with vertex $A$ and rays $AB$ and $AC$. - Taking $A$ as center and a suitable radius, draw an arc intersecting $AB$ and $AC$ at points $X$ and $Y$. - Taking $O$ as center and the same radius, draw an arc intersecting ray $OP$ at point $M$. - Measure the length $XY$ using a compass. - Taking $M$ as center and $XY$ as radius, draw an arc intersecting the arc from $O$ at point $N$. - Join points $O$ and $N$ and extend to $Q$. 4. **Result:** $\angle POQ$ is equal to $\angle BAC$. This method copies the angle by replicating the arc and the chord length, ensuring the new angle is congruent.