1. **Problem statement:** Bisect the angle $\angle ZXY$ in the given diagram and explain how to check if the bisection is accurate. 2. **Understanding angle bisector:** An angle bisector divides an angle into two equal smaller angles. 3. **Steps to bisect $\angle ZXY$:** - Place the compass point at vertex $X$. - Draw an arc that intersects both rays $XZ$ and $XY$ at points $A$ and $B$ respectively. - Without changing the compass width, place the compass point at $A$ and draw an arc inside the angle. - Repeat from point $B$ to intersect the previous arc at point $C$. - Draw a straight line from $X$ through $C$. This line bisects $\angle ZXY$. 4. **Checking accuracy:** - Measure the angles $\angle ZXC$ and $\angle CXY$ using a protractor. - If the two angles are equal, the bisection is accurate. 5. **Summary:** The bisector line $XC$ divides $\angle ZXY$ into two equal angles, confirming the bisection.