Question

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

Explanation:

Step1: Sum of angles in a triangle

The sum of angles in a triangle is \(180^{\circ}\). So, \(65^{\circ}+3z + 2z=180^{\circ}\).

Step2: Combine like - terms

Combine \(3z\) and \(2z\). We get \(65^{\circ}+5z = 180^{\circ}\).

Step3: Isolate the variable term

Subtract \(65^{\circ}\) from both sides. \(5z=180^{\circ}- 65^{\circ}\), so \(5z = 115^{\circ}\).

Step4: Solve for \(z\)

Divide both sides by \(5\). \(z=\frac{115^{\circ}}{5}\).

Answer:

\(z = 23\)