Question

what is the value of w?
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Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(w + 44^{\circ}=(w - 23^{\circ})+(w - 28^{\circ})\)

Step2: Expand the right - hand side

\(w+44^{\circ}=w - 23^{\circ}+w - 28^{\circ}\)
\(w + 44^{\circ}=2w-(23^{\circ}+28^{\circ})\)
\(w + 44^{\circ}=2w - 51^{\circ}\)

Step3: Solve for \(w\)

Subtract \(w\) from both sides:
\((w - w)+44^{\circ}=2w - w-51^{\circ}\)
\(44^{\circ}=w - 51^{\circ}\)
Add \(51^{\circ}\) to both sides:
\(w=44^{\circ}+51^{\circ}\)
\(w = 95^{\circ}\)

Answer:

\(95\)