Question

the diagram shows a triangle. what is the value of b? write your answer as an integer or as a decimal rounded to the nearest tenth. b =

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(31+(2b + 12)+(2b-12)=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \(31+2b + 12+2b-12=(2b+2b)+(12 - 12)+31\).
\(4b+31 = 180\).

Step3: Solve for \(b\)

Subtract 31 from both sides of the equation: \(4b=180 - 31\).
\(4b=149\).
Then divide both sides by 4: \(b=\frac{149}{4}=37.25\).

Answer:

\(b = 37.25\)