Question

what is the value of b? image of a triangle with angles labeled ( b ), ( 2b - 24^circ ), and an exterior angle ( b + 36^circ ) ( b = square^circ ) submit

Explanation:

Step1: Use 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, we have the equation $b + 36^{\circ}=b+(2b - 24^{\circ})$

Step2: Simplify the equation

First, simplify the right - hand side of the equation: $b+(2b - 24^{\circ})=3b-24^{\circ}$
So our equation becomes $b + 36^{\circ}=3b-24^{\circ}$

Step3: Solve for b

Subtract $b$ from both sides: $36^{\circ}=2b-24^{\circ}$
Add $24^{\circ}$ to both sides: $36^{\circ}+ 24^{\circ}=2b$
$60^{\circ}=2b$
Divide both sides by 2: $b=\frac{60^{\circ}}{2}=30^{\circ}$

Answer:

$30$