Question

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

Explanation:

Step1: Use the triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((b + 17)+(3b + 4)+(2b-27)=180\).

Step2: Combine like - terms

First, expand the left - hand side: \(b + 17+3b + 4+2b-27=(b + 3b+2b)+(17 + 4-27)=6b-6\).
So, the equation becomes \(6b-6 = 180\).

Step3: Solve for \(b\)

Add \(6\) to both sides of the equation: \(6b-6 + 6=180 + 6\), which gives \(6b=186\).
Then divide both sides by \(6\): \(b=\frac{186}{6}\).

Answer:

\(b = 31\)