Question

a triangle has interior angle measures of 45°, w - 15°, and 2w - 12°. what is the value of w? write your answer as an integer or as a decimal rounded to the nearest tenth. w =

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(45+(w - 15)+(2w-12)=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms:

$$
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Step3: Solve for \(w\)

Subtract \(18\) from both sides of the equation \(18 + 3w=180\):
\(3w=180 - 18=162\).
Then divide both sides by \(3\): \(w=\frac{162}{3}=54\).

Answer:

\(54\)