Question

what is the value of b?

Explanation:

Step1: Find total interior angles

First, count the sides: this is an 8-sided polygon (octagon). The formula for total interior angles is $(n-2)\times180^\circ$, where $n=8$.
$$(8-2)\times180^\circ = 6\times180^\circ = 1080^\circ$$

Step2: Sum all given angles

Add up all the angle expressions:
$$150^\circ + (b+50^\circ) + 2b + (2b+10^\circ) + (b+50^\circ) + (b+50^\circ) + 2b + 2b$$
Combine like terms:
$$150+50+10+50+50 + (b+2b+2b+b+b+2b+2b) = 360^\circ + 11b$$

Step3: Set equal to total, solve for b

Equate the sum to $1080^\circ$:
$$360 + 11b = 1080$$
Subtract 360 from both sides:
$$11b = 1080 - 360 = 720$$
Divide by 11:
$$b = \frac{720}{11} \approx 65.45$$

Answer:

$b=\frac{720}{11}$ or approximately $65.45^\circ$