Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of interior angles in a triangle is \(180^{\circ}\). So, \(8w + 47^{\circ}+85^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

\(8w+(47 + 85)^{\circ}=180^{\circ}\), which gives \(8w+132^{\circ}=180^{\circ}\).

Step3: Solve for \(8w\)

Subtract \(132^{\circ}\) from both sides: \(8w=180^{\circ}-132^{\circ}\), so \(8w = 48^{\circ}\).

Step4: Solve for \(w\)

Divide both sides by \(8\): \(w=\frac{48^{\circ}}{8}\).

Answer:

\(6\)