Question

the diagram shows a triangle. what is the value of b?

Explanation:

Step1: Use triangle angle - sum theorem

The sum of interior angles of a triangle is \(180^{\circ}\). So, \(19b + 102^{\circ}+40^{\circ}=180^{\circ}\).

Step2: Simplify the equation

\(19b+142^{\circ}=180^{\circ}\). Then, \(19b = 180^{\circ}-142^{\circ}\).

Step3: Calculate the value of \(b\)

\(19b = 38^{\circ}\), so \(b=\frac{38}{19}\).

Answer:

\(b = 2\)