Question

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

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, if the angles of the triangle are \(z\), \(37^{\circ}\), and \(33^{\circ}\), then \(z + 37^{\circ}+33^{\circ}=180^{\circ}\).

Step2: Solve for \(z\)

First, simplify the left - hand side of the equation: \(z+(37 + 33)^{\circ}=180^{\circ}\), which gives \(z + 70^{\circ}=180^{\circ}\). Then, subtract \(70^{\circ}\) from both sides of the equation: \(z=180^{\circ}-70^{\circ}\).

Answer:

\(z = 110^{\circ}\)