Question

what is the value of b?

write your answer as an integer or as a decimal rounded to the nearest tenth.

b =

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(5b=(4b - 47)+3b\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(b\)

Subtract \(5b\) from both sides: \(0 = 2b-47\). Then add \(47\) to both sides: \(2b=47\). Divide both sides by \(2\): \(b=\frac{47}{2}=23.5\).

Answer:

\(23.5\)