what is the value of w?

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. So, ((w + 3)+(w + 44)+w=180).

Step2: Combine like - terms

Combine the (w) terms and the constant terms: ((1 + 1+1)w+(3 + 44)=180), which simplifies to (3w+47 = 180).

Step3: Isolate the variable term

Subtract 47 from both sides of the equation: (3w=180 - 47), so (3w=133).

Step4: Solve for (w)

Divide both sides by 3: (w=\frac{133}{3}\approx44.33).

Answer:

(w = \frac{133}{3})