1. **Problem statement:** Given $m \angle YXW = 21^\circ$, $YW = 5$, and $WZ = 5$, find $m \angle ZXY$ in triangle $XYZ$ with right angles at $W$. 2. **Understanding the problem:** Points $Y$, $W$, and $Z$ form right angles at $W$, and $YW = WZ = 5$ means $W$ is the midpoint of segment $YZ$ and $\triangle YWZ$ is isosceles right triangle. 3. **Key fact:** Since $YW = WZ$, triangle $YWZ$ is isosceles with $\angle YWZ = 90^\circ$, so $\triangle YWZ$ is a right isosceles triangle with legs 5. 4. **Find $m \angle ZXY$:** Note that $X$ is connected to $Y$ and $Z$, and $W$ lies on $YZ$ such that $YW = WZ$. 5. Since $m \angle YXW = 21^\circ$, and $W$ lies on $YZ$, $\angle ZXY$ is the angle adjacent to $\angle YXW$ at vertex $X$. 6. Because $W$ is midpoint of $YZ$, $\angle YXW$ and $\angle ZXY$ are complementary angles in triangle $XYZ$ (since $W$ lies on $YZ$ and $\angle YWZ = 90^\circ$). 7. Therefore, $$m \angle ZXY = 90^\circ - m \angle YXW = 90^\circ - 21^\circ = 69^\circ.$$