1. **State the problem:** We need to find the missing interior angle $d$ of a pentagon where the other four angles are $100^\circ$, $95^\circ$, $105^\circ$, and $150^\circ$. 2. **Formula for interior angles of a polygon:** The sum of interior angles of an $n$-sided polygon is given by: $$\text{Sum} = (n-2) \times 180^\circ$$ For a pentagon, $n=5$, so: $$\text{Sum} = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$$ 3. **Set up the equation:** The sum of all five interior angles must be $540^\circ$: $$100^\circ + 95^\circ + 105^\circ + 150^\circ + d = 540^\circ$$ 4. **Calculate the sum of known angles:** $$100^\circ + 95^\circ + 105^\circ + 150^\circ = 450^\circ$$ 5. **Solve for $d$:** $$450^\circ + d = 540^\circ$$ Subtract $450^\circ$ from both sides: $$\cancel{450^\circ} + d = 540^\circ - \cancel{450^\circ}$$ $$d = 90^\circ$$ **Final answer:** $$d = 90^\circ$$