Question

what is the value of b? image of a triangle with an exterior angle labeled ( b + 50^circ ), and two interior angles labeled ( 2b + 3^circ ) and ( 4b - 38^circ ) ( b = \boxed{^circ} ) submit

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 have the equation: $b + 50=(2b + 3)+(4b-38)$

Step2: Simplify the right - hand side

First, combine like terms on the right - hand side. $(2b + 3)+(4b-38)=2b+4b + 3-38=6b-35$
So the equation becomes $b + 50=6b-35$

Step3: Solve for b

Subtract $b$ from both sides: $50=6b - b-35$, which simplifies to $50 = 5b-35$
Then add 35 to both sides: $50 + 35=5b$, so $85 = 5b$
Divide both sides by 5: $b=\frac{85}{5}=17$

Answer:

$17$