Question

solve for the value of z.

Explanation:

Step1: Set up equation

The sum of the angles around a point is 360°. Here, we have a right - angle (90°) and two angles (5z + 7)° and (8z - 8)°. So, (5z + 7)+(8z - 8)+90 = 180 (since they form a straight - line pair and the sum of angles on a straight line is 180°).

Step2: Combine like terms

Combine the z - terms and the constant terms: (5z+8z)+(7 - 8)+90 = 180, which simplifies to 13z-1 + 90 = 180, and further to 13z+89 = 180.

Step3: Isolate the variable term

Subtract 89 from both sides of the equation: 13z+89 - 89=180 - 89, resulting in 13z = 91.

Step4: Solve for z

Divide both sides by 13: $\frac{13z}{13}=\frac{91}{13}$, so z = 7.

Answer:

7