Angle Value 01Afe1

1. **State the problem:** We need to find the value of $z$ given two angles $(5z+1)^\circ$ and $59^\circ$ that together form a right angle. 2. **Understand the geometry:** The problem shows a right angle formed by two rays, with a diagonal line splitting the right angle into two smaller angles: $(5z+1)^\circ$ and $59^\circ$. 3. **Use the angle sum rule:** The sum of the two smaller angles must equal the right angle, which is $90^\circ$. $$ (5z + 1) + 59 = 90 $$ 4. **Simplify the equation:** $$ 5z + 1 + 59 = 90 $$ $$ 5z + 60 = 90 $$ 5. **Isolate $z$:** $$ 5z = 90 - 60 $$ $$ 5z = 30 $$ 6. **Divide both sides by 5:** $$ z = \frac{30}{5} $$ $$ z = 6 $$ 7. **Final answer:** $$ \boxed{6} $$ Thus, the value of $z$ is 6.