1. **State the problem:** We are given a polygon with five interior angles measuring 65°, 88°, 152°, 96°, and an unknown angle $x$. We need to find the value of $x$. 2. **Formula used:** The sum of interior angles of a polygon with $n$ sides is given by: $$\text{Sum of interior angles} = (n-2) \times 180^\circ$$ 3. **Apply the formula:** Since the polygon has 5 sides, the sum of its interior angles is: $$ (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ $$ 4. **Set up the equation:** The sum of the known angles plus the unknown angle $x$ must equal 540°: $$ 65^\circ + 88^\circ + 152^\circ + 96^\circ + x = 540^\circ $$ 5. **Calculate the sum of known angles:** $$ 65 + 88 + 152 + 96 = 401 $$ 6. **Solve for $x$:** $$ x = 540 - 401 = 139 $$ 7. **Conclusion:** The unknown interior angle $x$ measures $139^\circ$. This makes sense because the polygon is concave near angle $x$, and concave polygons have at least one interior angle greater than 180°, but here $x$ is less than 180°, so the indentation is likely due to the shape rather than the angle measure exceeding 180°. **Final answer:** $$ x = 139^\circ $$