Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(37^\circ + 59^\circ + 12z = 180^\circ\).

Step2: Calculate sum of known angles

Add \(37\) and \(59\): \(37 + 59 = 96\). So, \(96 + 12z = 180\).

Step3: Solve for \(12z\)

Subtract \(96\) from both sides: \(12z = 180 - 96 = 84\).

Step4: Solve for \(z\)

Divide both sides by \(12\): \(z = \frac{84}{12} = 7\).

Answer:

\(7\)