Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(31^\circ + 113^\circ + 4z = 180^\circ\).

Step2: Simplify left - hand side

First, calculate \(31 + 113 = 144\). The equation becomes \(144 + 4z = 180\).

Step3: Solve for \(4z\)

Subtract \(144\) from both sides: \(4z = 180 - 144 = 36\).

Step4: Solve for \(z\)

Divide both sides by \(4\): \(z=\frac{36}{4}=9\).

Answer:

\(z = 9\)