Question

the diagram shows a triangle. 46° 16z−38° 76° what is the value of z? z = □° submit

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(46^\circ + 76^\circ + (16z - 38)^\circ = 180^\circ\).

Step2: Simplify the left side

Calculate \(46 + 76 - 38 = 84\), so the equation becomes \(84 + 16z = 180\).

Step3: Solve for z

Subtract 84 from both sides: \(16z = 180 - 84 = 96\). Then divide by 16: \(z = \frac{96}{16} = 6\).

Answer:

\(z = 6\)