Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((w + 10)+(4w-39)+(3w - 31)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((w+4w + 3w)+(10-39 - 31)=180\).
\(8w+(10-(39 + 31))=180\).
\(8w+(10 - 70)=180\).
\(8w-60 = 180\).

Step3: Solve for \(w\)

Add \(60\) to both sides of the equation: \(8w-60+60=180 + 60\).
\(8w=240\).
Divide both sides by \(8\): \(w=\frac{240}{8}\).

Answer:

\(30\)