Question

what is the value of s?

write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(4s=37+(2s - 2)\).

Step2: Simplify the equation

First, expand the right - hand side: \(4s=37 + 2s-2\). Then, combine like terms: \(4s=2s + 35\).

Step3: Solve for \(s\)

Subtract \(2s\) from both sides: \(4s-2s=2s + 35-2s\). This gives \(2s=35\). Divide both sides by \(2\): \(s=\frac{35}{2}=17.5\).

Answer:

\(17.5\)