Question

the diagram shows a triangle. what is the value of z? write your answer as an integer or as a decimal roun

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(2z+(z + 32)+72=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2z+z+32 + 72=180\), which gives \(3z+104 = 180\).

Step3: Solve for \(z\)

Subtract 104 from both sides: \(3z=180 - 104\), so \(3z=76\). Then divide both sides by 3: \(z=\frac{76}{3}\approx25.3\).

Answer:

\(z\approx25.3\)