Question

the diagram shows a triangle. what is the value of w? w =

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(32+(w - 17)+(2w-18)=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \(32 + w-17+2w - 18=(w + 2w)+(32-17 - 18)=3w+(15 - 18)=3w - 3\).
The equation becomes \(3w-3 = 180\).

Step3: Solve for \(w\)

Add \(3\) to both sides of the equation: \(3w-3 + 3=180 + 3\), which gives \(3w=183\).
Then divide both sides by \(3\): \(w=\frac{183}{3}\).

Answer:

\(61\)