Question

what is the value of s? write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(2s - 15=(s + 44)+(s + 10)\).

Step2: Simplify the right - hand side

\((s + 44)+(s + 10)=s + 44+s + 10=2s+54\). So the equation becomes \(2s - 15=2s + 54\). But this is incorrect. Let's assume the large triangle's angle sum property. The sum of interior angles of a triangle is \(180^{\circ}\). The third angle of the large triangle is \(180-(s + 44)=136 - s\). Then, \((2s-15)+(136 - s)+(s + 10)=180\).

Step3: Combine like terms

\(2s-15 + 136 - s+s + 10=180\). Combine the \(s\) terms: \((2s - s+s)+(-15 + 136+10)=180\), which simplifies to \(2s+131 = 180\).

Step4: Solve for \(s\)

Subtract 131 from both sides: \(2s=180 - 131\), so \(2s = 49\). Then \(s=\frac{49}{2}=24.5\).

Answer:

\(24.5\)