Question

what is the value of s? s + 34° 11s+35° 31° write your answer as an integer or as a decimal. s =

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let's assume the triangle has angles \(s + 34^{\circ}\), \(11s+35^{\circ}\), and \(31^{\circ}\). So, \((s + 34)+(11s + 35)+31=180\).

Step2: Combine like - terms

Combine the \(s\) terms and the constant terms: \((s+11s)+(34 + 35+31)=180\), which simplifies to \(12s+100 = 180\).

Step3: Isolate the variable \(s\)

Subtract 100 from both sides of the equation: \(12s=180 - 100\), so \(12s=80\). Then divide both sides by 12: \(s=\frac{80}{12}=\frac{20}{3}\approx6.67\). But if we assume this is a problem about the exterior - angle property (if the figure has an exterior - angle situation), we know that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let's assume \(11s + 35=(s + 34)+31\).

Step4: Solve the new equation

Expand the right - hand side: \(11s+35=s + 65\). Subtract \(s\) from both sides: \(11s - s+35=s - s + 65\), which gives \(10s+35 = 65\). Then subtract 35 from both sides: \(10s=65 - 35\), so \(10s=30\). Divide both sides by 10: \(s = 3\).

Answer:

\(s = 3\)