Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(37^{\circ}+113^{\circ}+6b = 180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add \(37^{\circ}\) and \(113^{\circ}\): \(37 + 113+6b=180\), which gives \(150+6b = 180\).

Step3: Solve for \(b\)

Subtract \(150\) from both sides of the equation: \(6b=180 - 150\). So, \(6b = 30\). Then divide both sides by \(6\): \(b=\frac{30}{6}\).

Answer:

\(b = 5\)