Question

what is the value of w? w + 47° w w - 43° w =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. The three angles of the triangle are \(w\), \(w - 43^{\circ}\), and the third - angle which is supplementary to \(w + 47^{\circ}\). The supplementary angle to \(w+47^{\circ}\) is \(180-(w + 47)=133 - w\).

Step2: Set up the equation

\(w+(w - 43)+(133 - w)=180\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \((w+w - w)+(-43 + 133)=180\), which simplifies to \(w + 90=180\).

Step4: Solve for \(w\)

Subtract 90 from both sides of the equation: \(w=180 - 90\).

Answer:

\(w = 90\)