Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, we add the three angles: \(42^\circ+(z + 14)^\circ+(z + 18)^\circ=180^\circ\).

Step2: Simplify the equation

Combine like terms: \(42+z + 14+z + 18 = 180\). Then, \(z+z+42 + 14+18=180\), which becomes \(2z+74 = 180\).

Step3: Solve for z

Subtract 74 from both sides: \(2z=180 - 74=106\). Then divide by 2: \(z=\frac{106}{2}=53\).

Answer:

\(z = 53\)