Question

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

Explanation:

Step1: Apply triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(34^{\circ}+38^{\circ}+18z = 180^{\circ}\).

Step2: Simplify the left - hand side

First, calculate \(34 + 38=72\). Then the equation becomes \(72+18z = 180\).

Step3: Solve for \(z\)

Subtract \(72\) from both sides: \(18z=180 - 72\). So, \(18z = 108\). Then divide both sides by \(18\): \(z=\frac{108}{18}\).

Answer:

\(z = 6\)