Question

what is the value of s?
write your answer as an integer or as a decimal rounded to the nearest tenth.
s+44°
5s+36°
14s+31°

Explanation:

Step1: Use 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, \(14s + 31=(s + 44)+(5s + 36)\)

Step2: Simplify the right - hand side of the equation

First, simplify \((s + 44)+(5s + 36)\):

$$
LATEXBLOCK0
$$

The equation becomes \(14s + 31=6s+80\)

Step3: Solve for \(s\)

Subtract \(6s\) from both sides: \(14s-6s + 31=6s-6s+80\), which gives \(8s+31 = 80\)
Subtract \(31\) from both sides: \(8s+31-31=80 - 31\), so \(8s=49\)
Divide both sides by \(8\): \(s=\frac{49}{8}=6.125\)

Answer:

\(6.1\)