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, \((w + 30)+2w+3w=180\).

Step2: Combine like terms

Combine the \(w\) terms: \(w+2w + 3w+30=180\), which simplifies to \(6w+30 = 180\).

Step3: Isolate the term with \(w\)

Subtract 30 from both sides: \(6w+30-30=180 - 30\), so \(6w=150\).

Step4: Solve for \(w\)

Divide both sides by 6: \(w=\frac{150}{6}\).

Answer:

\(25\)