Question

solve for x.
then find the measure of angle
hint: \13x - 3\ is an exterior a 2\ and \55\ are interior angles.

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, \(13x - 3=(3x + 2)+55\).

Step2: Simplify the equation

First, simplify the right - hand side: \((3x + 2)+55=3x+57\). Then the equation becomes \(13x - 3=3x + 57\).
Subtract \(3x\) from both sides: \(13x-3x - 3=3x-3x + 57\), which gives \(10x-3 = 57\).
Add \(3\) to both sides: \(10x-3 + 3=57 + 3\), so \(10x=60\).
Divide both sides by \(10\): \(x=\frac{60}{10}=6\).

Step3: Find the measure of \(\angle B\)

Substitute \(x = 6\) into the expression for \(\angle B\) (\(3x + 2\)).
\(\angle B=3\times6+2=18 + 2=20^{\circ}\).

Answer:

\(x = 6\) and the measure of \(\angle B\) is \(20^{\circ}\)