Question

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

Explanation:

Step1: Use the triangle angle sum theorem

The sum of angles in a triangle is \(180^{\circ}\). So, \((2s - 16)+2s+(2s - 20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2s-16 + 2s+2s - 20=(2s+2s+2s)+(-16 - 20)=6s-36\).
The equation becomes \(6s - 36 = 180\).

Step3: Solve for \(s\)

Add \(36\) to both sides: \(6s-36 + 36=180 + 36\), which gives \(6s=216\).
Divide both sides by \(6\): \(s=\frac{216}{6}\).

Answer:

\(s = 36\)