Question

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

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation

Let the three angles of the triangle be \(46^{\circ}\), \(31^{\circ}\), and \(z\). Then \(46 + 31+z=180\).

Step3: Solve for \(z\)

First, calculate \(46 + 31=77\). Then the equation becomes \(77+z = 180\). Subtract \(77\) from both sides: \(z=180 - 77\).

Answer:

\(z = 103\)