1. **Problem:** Find $m\widehat{WXZ}$ given $m\widehat{WZ} = 105^\circ$ in circle with points $W, X, Z$. 2. **Formula:** The measure of an arc around a circle is $360^\circ$. The arcs $WZ$ and $WXZ$ together form the entire circle, so $$m\widehat{WZ} + m\widehat{WXZ} = 360^\circ$$ 3. **Calculation:** Substitute the given value: $$105^\circ + m\widehat{WXZ} = 360^\circ$$ 4. **Isolate $m\widehat{WXZ}$:** $$m\widehat{WXZ} = 360^\circ - 105^\circ$$ 5. **Simplify:** $$m\widehat{WXZ} = 255^\circ$$ **Answer:** $m\widehat{WXZ} = 255^\circ$