Question

a triangle has interior angle measures of w + 15°, 2w, and w + 1°. 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, \((w + 15)+2w+(w + 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((w+2w + w)+(15 + 1)=180\), which gives \(4w+16 = 180\).

Step3: Solve for \(w\)

Subtract \(16\) from both sides: \(4w=180 - 16=164\). Then divide both sides by \(4\): \(w=\frac{164}{4}=41\).

Answer:

\(41\)