1. **State the problem:** We are given two angles expressed as $4(x + 1)^0$ and $(7x + 3)^0$ and asked to find the value of $x$. 2. **Interpret the notation:** The notation $( ext{expression})^0$ means the expression is raised to the power 0. Any nonzero number raised to the power 0 equals 1. 3. **Evaluate each angle:** - $4(x + 1)^0 = 4 \times 1 = 4$ - $(7x + 3)^0 = 1$ 4. **Analyze the problem:** Since the angles are labeled as $4$ and $1$ degrees, but angles in degrees cannot be 1 degree and 4 degrees if they are equal or supplementary, the problem likely means the expressions inside the parentheses are angles in degrees, and the exponent 0 is a notation error or means something else. 5. **Assuming the exponent 0 means degrees (° symbol):** Then the angles are $4(x + 1)^ ext{degrees}$ and $(7x + 3)^ ext{degrees}$. 6. **If the two angles are equal (since they intersect and are labeled), set them equal:** $$4(x + 1) = 7x + 3$$ 7. **Solve for $x$:** $$4x + 4 = 7x + 3$$ $$4x + 4 - 7x - 3 = 0$$ $$-3x + 1 = 0$$ $$-3x = -1$$ $$x = \frac{1}{3}$$ **Final answer:** $$x = \frac{1}{3}$$