Question

the diagram shows a triangle. what is the value of z?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \((z + 3)+(z - 18)+(z - 9)=180\).

Step2: Combine like - terms

\(z+z + z+3-18 - 9=180\), which simplifies to \(3z-24 = 180\).

Step3: Isolate the variable term

Add 24 to both sides of the equation: \(3z-24 + 24=180 + 24\), resulting in \(3z=204\).

Step4: Solve for z

Divide both sides by 3: \(\frac{3z}{3}=\frac{204}{3}\), so \(z = 68\).

Answer:

68