Question

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

Explanation:

Step1: Apply exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, we set up the equation $13x−3=(3x + 2)+55$.

Step2: Simplify the right - hand side of the equation

$(3x + 2)+55=3x+57$. So the equation becomes $13x−3 = 3x+57$.

Step3: Isolate the variable terms

Subtract $3x$ from both sides: $13x−3x−3=3x−3x + 57$, which simplifies to $10x−3=57$.

Step4: Isolate the variable

Add 3 to both sides: $10x−3 + 3=57+3$, getting $10x=60$.

Step5: Solve for x

Divide both sides by 10: $\frac{10x}{10}=\frac{60}{10}$, so $x = 6$.

Step6: Find the measure of angle FAB

Substitute $x = 6$ into the expression for angle FAB, which is $13x−3$. So, $13\times6−3=78 - 3=75$.

Answer:

$x = 6$, measure of angle FAB is $75^{\circ}$