Question

a triangle has interior angle measures of 54°, w, and 83°. what is the value of w?

w = □°

Explanation:

Step1: Recall the sum of interior angles of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(54^{\circ}+w + 83^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add \(54^{\circ}\) and \(83^{\circ}\): \(54 + 83=137\), so the equation becomes \(137^{\circ}+w=180^{\circ}\).

Step3: Solve for \(w\)

Subtract \(137^{\circ}\) from both sides of the equation: \(w=180^{\circ}-137^{\circ}\).
\(w = 43^{\circ}\)

Answer:

\(43\)