1. **State the problem:** We are given that $m\angle WXZ = 95^\circ$ and $m\angle 1$ is 27° more than $m\angle 2$. We need to find $m\angle 2$. 2. **Understand the angles:** $\angle WXZ$ is the larger angle formed by rays $XW$ and $XZ$. Inside this angle, there are two smaller angles $\angle 1$ and $\angle 2$ formed by rays $XY$ with $XZ$ and $XW$ respectively. 3. **Write the relationship:** Since $\angle 1$ and $\angle 2$ are adjacent and together form $\angle WXZ$, we have: $$m\angle 1 + m\angle 2 = m\angle WXZ$$ 4. **Express $m\angle 1$ in terms of $m\angle 2$:** Given $m\angle 1$ is 27° more than $m\angle 2$, so: $$m\angle 1 = m\angle 2 + 27$$ 5. **Substitute into the sum equation:** $$ (m\angle 2 + 27) + m\angle 2 = 95 $$ 6. **Combine like terms:** $$ 2m\angle 2 + 27 = 95 $$ 7. **Isolate $m\angle 2$:** $$ 2m\angle 2 = 95 - 27 $$ $$ 2m\angle 2 = 68 $$ 8. **Divide both sides by 2:** $$ m\angle 2 = \frac{68}{2} $$ $$ m\angle 2 = 34 $$ **Final answer:** $$m\angle 2 = 34^\circ$$