Question

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

Explanation:

Step1: Use the triangle angle sum property

The sum of angles in a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A = 31^{\circ}\), \(B=99^{\circ}\), and \(C = 10s\). Then the equation is \(A + B + C=180^{\circ}\).

Step2: Substitute the values into the equation

Substitute \(A = 31\), \(B = 99\), and \(C = 10s\) into \(A + B + C = 180\). We get \(31+99 + 10s=180\).

Step3: Simplify the left - hand side

First, calculate \(31 + 99=130\). So the equation becomes \(130+10s = 180\).

Step4: Solve for \(s\)

Subtract \(130\) from both sides: \(10s=180 - 130\). Then \(10s = 50\). Divide both sides by \(10\): \(s=\frac{50}{10}\).

Answer:

\(s = 5\)