Question

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

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((9s - 11)+(2s + 20)+50=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((9s+2s)+(-11 + 20+50)=180\), which gives \(11s+(9 + 50)=180\), and then \(11s+59 = 180\).

Step3: Solve for \(s\)

Subtract 59 from both sides: \(11s=180 - 59\), so \(11s=121\). Then divide both sides by 11: \(s=\frac{121}{11}\).

Answer:

\(s = 11\)