Question

the diagram shows a triangle. what is the value of s? s =

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((s + 31^{\circ})+(s + 21^{\circ})+(s+35^{\circ})=180^{\circ}\).

Step2: Combine like terms

Combine the \(s\) terms and the constant terms: \(3s+(31 + 21+35)^{\circ}=180^{\circ}\), which simplifies to \(3s + 87^{\circ}=180^{\circ}\).

Step3: Solve for \(s\)

Subtract \(87^{\circ}\) from both sides: \(3s=180^{\circ}- 87^{\circ}\), so \(3s = 93^{\circ}\). Then divide both sides by \(3\): \(s=\frac{93^{\circ}}{3}\).

Answer:

\(s = 31\)