Question

what is the value of b?
(there is a triangle with an exterior angle and some angle expressions: one angle inside the triangle is 3b - 11°, another inside angle is 3b, and the exterior angle is 3b + 37°)
write your answer as an integer or as a decimal rounded to the nearest tenth.
( b = square^circ )
submit

Explanation:

Step1: Apply exterior angle theorem

The exterior angle of a triangle equals the sum of the two opposite interior angles, so:
$$3b + 37^\circ = (2b - 11^\circ) + 3b$$

Step2: Simplify the right-hand side

Combine like terms on the right:
$$3b + 37^\circ = 5b - 11^\circ$$

Step3: Isolate terms with $b$

Subtract $3b$ from both sides:
$$37^\circ = 2b - 11^\circ$$

Step4: Solve for $2b$

Add $11^\circ$ to both sides:
$$2b = 37^\circ + 11^\circ = 48^\circ$$

Step5: Calculate $b$

Divide both sides by 2:
$$b = \frac{48^\circ}{2} = 24^\circ$$

Answer:

$24$