Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(57^{\circ}+2z+(z - 15^{\circ})=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(57-15 + 2z+z=180\), which gives \(42 + 3z=180\).

Step3: Solve for \(z\)

Subtract \(42\) from both sides: \(3z=180 - 42\), so \(3z=138\). Then divide both sides by \(3\): \(z=\frac{138}{3}\).

Answer:

\(46\)