Question

what is the value of w? w + 2° w + 48° w + 14° w =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. For the larger triangle, the three angles are \(w + 2\), \(w+48\) and \(w + 14\). So, \((w + 2)+(w + 48)+(w+14)=180\).

Step2: Combine like - terms

\[

$$\begin{align*} w+2+w + 48+w+14&=180\\ 3w+(2 + 48+14)&=180\\ 3w + 64&=180 \end{align*}$$

\]

Step3: Isolate the variable term

Subtract 64 from both sides of the equation: \(3w=180 - 64\), so \(3w=116\).

Step4: Solve for \(w\)

Divide both sides by 3: \(w=\frac{116}{3}\approx38.67\).

Answer:

\(w = \frac{116}{3}\)