Question

solve for the value of z.

Explanation:

Step1: Recognize the right angle

The two angles \( (8z)^\circ \) and \( (3z + 2)^\circ \) add up to \( 90^\circ \) because they form a right angle. So we set up the equation: \( 8z + (3z + 2) = 90 \).

Step2: Combine like terms

Combine the \( z \)-terms: \( 8z + 3z + 2 = 90 \) simplifies to \( 11z + 2 = 90 \).

Step3: Subtract 2 from both sides

Subtract 2 from each side: \( 11z + 2 - 2 = 90 - 2 \), which gives \( 11z = 88 \).

Step4: Divide by 11

Divide both sides by 11: \( \frac{11z}{11} = \frac{88}{11} \), so \( z = 8 \).

Answer:

\( z = 8 \)