Question

what is the value of s? a triangle with an exterior angle. the exterior angle is labeled 4s. the two non-adjacent interior angles are labeled s + 18° and 2s + 3°.

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, we have the equation $4s=(s + 18^{\circ})+(2s+3^{\circ})$.

Step2: Simplify the right - hand side of the equation

First, combine like terms on the right - hand side: $(s + 18^{\circ})+(2s+3^{\circ})=s+2s + 18^{\circ}+3^{\circ}=3s+21^{\circ}$. So our equation becomes $4s=3s + 21^{\circ}$.

Step3: Solve for s

Subtract $3s$ from both sides of the equation $4s=3s + 21^{\circ}$. We get $4s-3s=3s + 21^{\circ}-3s$, which simplifies to $s = 21^{\circ}$.

Answer:

The value of \(s\) is \(21\) (when considering the unit as degrees, the value of \(s\) is \(21\)).