Question

what is the value of b?
triangle with angles: 30b - 59°, 35°, and an exterior angle b + 100°
write your answer as an integer or as a decimal rounded to the nearest tenth.
b = \boxed{}°

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles, so:
$$b + 100 = (30b - 59) + 35$$

Step2: Simplify right-hand side

Combine the constant terms:
$$b + 100 = 30b - 24$$

Step3: Isolate variable terms

Subtract $b$ from both sides:
$$100 = 29b - 24$$

Step4: Isolate constant terms

Add 24 to both sides:
$$124 = 29b$$

Step5: Solve for $b$

Divide both sides by 29:
$$b = \frac{124}{29}$$

Answer:

$4.3$