Question

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

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(3z + 2z+76^{\circ}=180^{\circ}\).

Step2: Combine like terms

\(5z+76^{\circ}=180^{\circ}\).

Step3: Solve for \(z\)

Subtract \(76^{\circ}\) from both sides: \(5z = 180^{\circ}-76^{\circ}\), \(5z=104^{\circ}\). Then divide both sides by \(5\): \(z=\frac{104^{\circ}}{5} = 20.8^{\circ}\).

Answer:

\(20.8\)