Question

the diagram shows a triangle. what is the value of z? z = \boxed{}

Explanation:

Step1: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \((z + 29)+43 + 11z=180\).

Step2: Combine like terms

Combine \(z\) and \(11z\), and constants. \(z+11z+29 + 43=180\), which simplifies to \(12z+72 = 180\).

Step3: Isolate the variable term

Subtract \(72\) from both sides: \(12z=180 - 72\). So, \(12z=108\).

Step4: Solve for \(z\)

Divide both sides by \(12\): \(z=\frac{108}{12}\).

Answer:

\(z = 9\)